Journal articles: 'Iteratie'

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Barakat, Saman A., and Qusay I. Sarhan. "Performance evaluation of list iteration methods in Java: an empirical study." Innovaciencia Facultad de Ciencias Exactas, Físicas y Naturales 6, no. 1 (December 28, 2018): 1–6. http://dx.doi.org/10.15649/2346075x.467.

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Introduction: Lists are used in various software applications including web applications, desktop applications, and Internet of Things (IoT) applications to store different types of items (e.g. country name, product model, and device category). Users can select one or more of these items to perform specific tasks such as filling forms, ordering products, reading device data, etc. In some software applications, lists store a huge number of items to be iterated over in order to know what users have selected. From a software development perspective, there are a number of methods to iterate over list items. Materials and Methods: In this paper, five list iteration methods: Classic For, Enhanced For, Iterator, List Iterator, and For Each have been compared experimentally with each other with regard to their performance (execution time required to iterate over list items). Thus, a number of experimental test scenarios have been conducted to obtain comparable results. Results and Discussion: The experimental results of this study have been presented in Table 4. Conclusions: Overall performance evaluation showed that Iterator and List Iterator methods outperformed other list iteration methods in all test scenarios. However, List Iterator outperformed Iterator when the list size was small. On the other hand, Iterator outperformed List Iterator when the list size was large.

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Kelly, Terence, and Kai Nagel. "Relaxation Criteria for Iterated Traffic Simulations." International Journal of Modern Physics C 09, no. 01 (February 1998): 113–32. http://dx.doi.org/10.1142/s0129183198000108.

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Iterative transportation microsimulations adjust traveler route plans by iterating between a microsimulation and a route planner. At each iteration, the route planner adjusts individuals' route choices based on the preceding microsimulations. Empirically, this process yields good results, but it is usually unclear when to stop the iterative process when modeling real-world traffic. This paper investigates several criteria to judge relaxation of the iterative process, emphasizing criteria related to traveler decision-making.

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Liu, Xiao-hua. "Iteration and Iterative Roots of Fractional Polynomial Function." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/365956.

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Iteration is involved in the fields of dynamical systems and numerical computation and so forth. The computation of iteration is difficult for general functions (even for some simple functions such as linear fractional functions). In this paper, we discuss fractional polynomial function and use the method of conjugate similitude to obtain its expression of general iterate of ordernunder two different conditions. Furthermore, we also give iterative roots of ordernfor the function under two different conditions.

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Wang, Feng, Jianping Zhang, Guiling Sun, and Tianyu Geng. "Iterative Forward-Backward Pursuit Algorithm for Compressed Sensing." Journal of Electrical and Computer Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/5940371.

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It has been shown that iterative reweighted strategies will often improve the performance of many sparse reconstruction algorithms. Iterative Framework for Sparse Reconstruction Algorithms (IFSRA) is a recently proposed method which iteratively enhances the performance of any given arbitrary sparse reconstruction algorithm. However, IFSRA assumes that the sparsity level is known. Forward-Backward Pursuit (FBP) algorithm is an iterative approach where each iteration consists of consecutive forward and backward stages. Based on the IFSRA, this paper proposes the Iterative Forward-Backward Pursuit (IFBP) algorithm, which applies the iterative reweighted strategies to FBP without the need for the sparsity level. By using an approximate iteration strategy, IFBP gradually iterates to approach the unknown signal. Finally, this paper demonstrates that IFBP significantly improves the reconstruction capability of the FBP algorithm, via simulations including recovery of random sparse signals with different nonzero coefficient distributions in addition to the recovery of a sparse image.

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Kheirfam, Behrouz. "Simplified analysis of a full Nesterov–Todd step infeasible interior-point method for symmetric optimization." Asian-European Journal of Mathematics 08, no. 04 (November 17, 2015): 1550071. http://dx.doi.org/10.1142/s1793557115500710.

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We give a simplified analysis and an improved iteration bound of a full Nesterov–Todd (NT) step infeasible interior-point method for solving symmetric optimization. This method shares the features as, it (i) requires strictly feasible iterates on the central path of a perturbed problem, (ii) uses the feasibility steps to find strictly feasible iterates for the next perturbed problem, (iii) uses the centering steps to obtain a strictly feasible iterate close enough to the central path of the new perturbed problem, and (iv) reduces the size of the residual vectors with the same speed as the duality gap. Furthermore, the complexity bound coincides with the currently best-known iteration bound for full NT step infeasible interior-point methods.

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Titaley, Jullia, Tohap Manurung, and Henriette D. Titaley. "CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTION." JURNAL ILMIAH SAINS 18, no. 2 (November 12, 2018): 103. http://dx.doi.org/10.35799/jis.18.2.2018.21555.

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CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTIONABSTRACTJulia set are defined by iterating a function of a complex number and is generated from the iterated function . We investigate in this paper the complex dynamics of different functions and applied iteration function system to generate an entire new class of julia set. The purpose of this research is to make variation of Cubic and Quadratic polynomial on Julia Set and the two obvious to investigate from julia set are Sine and Cosine function. The results thus obtained are innovative and studies about different behavior of two basic trigonometry.Keywords : Julia Set, trigonometric function, polynomial function POLINOMIAL KUBIK DAN KUADRATIK PADA HIMPUNAN JULIA DENGAN FUNGSI TRIGONOMETRI ABSTRAKHimpunan Julia didefiniskan oleh fungsi iterasi dari bilangan kompleks dan dibangkitkan dari fungsi iterasi . Kami melakukan penelitian dalam penulisan ini tentang sistem dinamik kompleks dari fungsi yang berbeda dengan iterasi yang diterapkan untuk menghasilkan kelas baru dari himpunan Julia. Tujuan dari penelitian ini adalah untuk membuah kelas baru himpunan Julia dengan fungsi polinomial kubik dan kuadratik dengan fungsi sinus dan kosinus. Hasil akhir dari penelitian ini ada menemukan inovatif baru dari himpunan Julia dengan menggunakan dua fungsi trigonometri.Kata kunci: Julia set, fungsi trigonometri, fungsi polinomial

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Burkart, Uhland. "Orbit entropy in noninvertible mappings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (February 1986): 95–110. http://dx.doi.org/10.1017/s1446788700026537.

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AbstractBassed on the intrinsic structure of a selfmapping T: S → S of an arbitrary set S, called the orbit-structure of T, a new entropy is defined. The idea is to use the number of preimages of an element x under the iterates of T to characterize the complexity of the transformation T and their orbit graphs. The fundamental properties of the orbit entropy related to iteration, iterative roots and iteration semigroups are studied. For continuous (differentiable) functions of Rn to Rn, the chaos of Li and Yorke is characterized by means of this entropy, mainly using the method of Straffingraphs.

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Abdeljawad, Thabet, and Arran Fernandez. "On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels." Mathematics 7, no. 9 (August 22, 2019): 772. http://dx.doi.org/10.3390/math7090772.

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We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.

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SARGSYAN, GRIGOR, and RALF SCHINDLER. "VARSOVIAN MODELS I." Journal of Symbolic Logic 83, no. 2 (June 2018): 496–528. http://dx.doi.org/10.1017/jsl.2018.5.

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AbstractLet Msw denote the least iterable inner model with a strong cardinal above a Woodin cardinal. By [11], Msw has a fully iterable core model, ${K^{{M_{{\rm{sw}}}}}}$, and Msw is thus the least iterable extender model which has an iterable core model with a Woodin cardinal. In V, ${K^{{M_{{\rm{sw}}}}}}$ is an iterate of Msw via its iteration strategy Σ.We here show that Msw has a bedrock which arises from ${K^{{M_{{\rm{sw}}}}}}$ by telling ${K^{{M_{{\rm{sw}}}}}}$ a specific fragment ${\rm{\bar{\Sigma }}}$ of its own iteration strategy, which in turn is a tail of Σ. Hence Msw is a generic extension of $L[{K^{{M_{{\rm{sw}}}}}},{\rm{\bar{\Sigma }}}]$, but the latter model is not a generic extension of any inner model properly contained in it.These results generalize to models of the form Ms (x) for a cone of reals x, where Ms (x) denotes the least iterable inner model with a strong cardinal containing x. In particular, the least iterable inner model with a strong cardinal above two (or seven, or boundedly many) Woodin cardinals has a 2-small core model K with a Woodin cardinal and its bedrock is again of the form $L[K,{\rm{\bar{\Sigma }}}]$.

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SALAHI, MAZIAR, and TAMÁS TERLAKY. "A HYBRID ADAPTIVE ALGORITHM FOR LINEAR OPTIMIZATION." Asia-Pacific Journal of Operational Research 26, no. 02 (April 2009): 235–56. http://dx.doi.org/10.1142/s0217595909002183.

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Recently, using the framework of self-regularity, Salahi in his Ph.D. thesis proposed an adaptive single step algorithm which takes advantage of the current iterate information to find an appropriate barrier parameter rather than using a fixed fraction of the current duality gap. However, his algorithm might do at most one bad step after each good step in order to keep the iterate in a certain neighborhood of the central path. In this paper, using the same framework, we propose a hybrid adaptive algorithm. Depending on the position of the current iterate, our new algorithm uses either the classical Newton search direction or a self-regular search direction. The larger the distance from the central path, the larger the barrier degree of the self-regular search direction is. Unlike the classical approach, here we control the iterates by guaranteeing certain reduction of the proximity measure. This itself leads to a one dimensional equation which determines the target barrier parameter at each iteration. This allows us to have a large update algorithm without any need for safeguard or special steps. Finally, we prove that our hybrid adaptive algorithm has an [Formula: see text] worst case iteration complexity.

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Conrad, M., T. Behr, S. Gratz, H. Luig, W. Becker, and J. Meiler. "Bedeutung der iterativen Rekonstruktion ISA bei der Diagnostik von Leberhämangiomen." Nuklearmedizin 36, no. 02 (1997): 65–70. http://dx.doi.org/10.1055/s-0038-1629736.

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Zusammenfassung Ziel: In dieser Studie sollte überprüft werden, ob das iterative Rekonstruktionsverfahren ISA Vorteile gegenüber der Standardmethode der gefilterten Rückprojektion besitzt. Methoden: Die Aufnahmen von 39 Patienten mit solitären oder multiplen Raumforderungen der Leber, bei denen eine Leberblutpoolszintigraphie in SPECT-Technik zum Nachweis oder Ausschluß von Leberhämangiomen durchgeführt worden war, wurden retrospektiv ausgewertet. Ergebnisse: Aktivitätsmehranreicherungen, die mit einem Leberhämangiom vereinbar waren, konnten durch die iterative Rekonstruktion bei 34 Herden und mittels gefilterter Rückprojektion bei 31 Herden in allen drei Schnittebenen dargestellt werden. Im Vergleich zur gefilterten Rückprojektion stellten sich die Läsionen nach iterativer Rekonstruktion meist kontrastreicher dar und waren von benachbarten Strukturen besser abzugrenzen. Darüber hinaus zeichnete sich das iterative Verfahren durch eine homogenere Aktivitätsbelegung der Leber aus. Die unregelmäßige Strukturierung des Leberparenchyms, wie sie sich nach gefilterter Rückprojektion fast regelhaft ergab, erschwerte hingegen häufig die sichere Trennung von Rekonstruktionsartefakten und Herdbefunden. Durch unseren iterativen Algorithmus konnte eine klarere Abbildung der Gefäße und eine verbesserte Abgrenzbarkeit der rechten Niere vom Leberparenchym erreicht werden, woraus sich Vorteile bei der Erkennung von zentral oder dorsal im rechten Leberlappen gelegenen Aktivitätsanreicherungen ergeben. Schlußfolgerung: Die vorgelegten Ergebnisse belegen, daß durch den Einsatz des iterativen Algorithmus bei der Leberblutpool-SPECT eine verbesserte Sensitivität und höhere diagnostische Sicherheit bei der Diagnostik von Leberhämangiomen erreicht werden kann.

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Cordero, Alicia, Javier G. Maimó, Juan R. Torregrosa, and María P. Vassileva. "Iterative Methods with Memory for Solving Systems of Nonlinear Equations Using a Second Order Approximation." Mathematics 7, no. 11 (November 7, 2019): 1069. http://dx.doi.org/10.3390/math7111069.

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Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable behavior in the sense of the wideness of the set of convergent initial estimations. With the right choice of parameters, iterative methods without memory can increase their order of convergence significantly, becoming schemes with memory. In this work, starting from a simple method without memory, we increase its order of convergence without adding new functional evaluations by approximating the accelerating parameter with Newton interpolation polynomials of degree one and two. Using this technique in the multidimensional case, we extend the proposed method to systems of nonlinear equations. Numerical tests are presented to verify the theoretical results and a study of the dynamics of the method is applied to different problems to show its stability.

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Li, Linxin, and Dingping Wu. "The Convergence of Three-Step Iterative Schemes for Generalized Φ − Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence." Journal of Mathematics 2021 (July 21, 2021): 1–14. http://dx.doi.org/10.1155/2021/9064369.

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Charles proved the convergence of Picard-type iteration for generalized Φ − accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ − quasi-accretive mappings and fixed points of strongly Φ − hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ − hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.

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ASO, HIROMOTO, and NAMIO HONDA. "REPRESENTATION OF ITERATIVE PATTERNS." International Journal of Pattern Recognition and Artificial Intelligence 03, no. 03n04 (December 1989): 479–95. http://dx.doi.org/10.1142/s021800148900036x.

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Iterative patterns can be described by the component pattern of iteration and their way of connection for iteration. It is shown that the shape of the component pattern can be a rectangle for any iterative pattern, which is called a tile. The tile is related to the basis of the parallel translation group of the iterative pattern. The component pattern itself is identified by a "tessera" which is defined by a non-degenerate colored tile. The tessera is a compact representation of iterative patterns. Some natures of tesseras and tiles are also discussed. The number of the kinds of distinct iterative patterns for each way of iteration is evaluated.

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Huang, Yin, Rami Nammour, and William Symes. "Flexibly preconditioned extended least-squares migration in shot-record domain." GEOPHYSICS 81, no. 5 (September 2016): S299—S315. http://dx.doi.org/10.1190/geo2016-0023.1.

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We have developed a method for accelerating the convergence of iterative least-squares migration. The algorithm uses a pseudodifferential scaling (dip and spatially varying filter) preconditioner together with a variant of conjugate gradient (CG) iteration with iterate-dependent (flexible) preconditioning. The migration is formulated without the image stack, thus producing a shot-dependent image volume that retains offset information useful for velocity updating and amplitude variation with offset analysis. Numerical experiments indicate that flexible preconditioning with pseudodifferential scaling not only attains considerably smaller data misfit and gradient error for a given computational effort, but also produces higher resolution image volumes with more balanced amplitude and fewer artifacts than is achieved with a nonpreconditioned CG method.

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ÉSIK, Z., and T. HAJGATÓ. "Dagger extension theorem." Mathematical Structures in Computer Science 21, no. 5 (August 22, 2011): 1035–66. http://dx.doi.org/10.1017/s0960129511000326.

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Partial iterative theories are algebraic theories such that for certain morphisms f the equation ξ = f ⋅ 〈ξ, 1p〉 has a unique solution. Iteration theories are algebraic theories satisfying a certain set of identities. We investigate some similarities between partial iterative theories and iteration theories.In our main result, we give a sufficient condition ensuring that the partially defined dagger operation of a partial iterative theory can be extended to a totally defined operation so that the resulting theory becomes an iteration theory. We show that this general extension theorem can be instantiated to prove that every Elgot iterative theory with at least one constant morphism 1 → 0 can be extended to an iteration theory. We also apply our main result to theories equipped with an additive structure.

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Wahab, O. T., R. O. Olawuyi, K. Rauf, and I. F. Usamot. "Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces." Journal of Mathematics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/9641706.

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This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that S-iteration converges faster than other iterations followed by Picard-Mann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among two-step iterative fixed point schemes in the literature.

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Thalib, Rehana, Maharani Abu Bakar, and Nur Fadhilah Ibrahim. "Application of Support Vector Regression in Krylov Solvers." Annals of Emerging Technologies in Computing 5, no. 5 (March 20, 2021): 178–86. http://dx.doi.org/10.33166/aetic.2021.05.022.

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Support vector regression (SVR) is well known as a regression or prediction tool under the Machine Learning (ML) which preserves all the key features through the training data. Different from general prediction, here, we proposed SVR to predict the new approximate solutions after we generated some iterates using an iterative method called Lanczos algorithm, one class of Krylov solvers. As we know that all Krylov solvers, including Lanczos methods, for solving the high dimensions of systems of linear equations (SLEs) problems experiences breakdown which causes the sequence of the iterates is incomplete, or the good approximate solution is never reached. By assuming that some iterates exist after the breakdown, then we could predict what they are. It is realized by learning the previous iterates generated by the Lanczos solvers, which is also called the training data. The SVR is then used to predict the next iterate which is expected the sequence now has similar property as the previous one before breaking down. Furthermore, we implemented the hybrid SVR-Lanczos (or SVR-L) in the restarting frame work, then it is called as hybrid restarting-SVR-L. The idea behind the restarting is that one time running hybrid SVR-L cannot obtain a good approximate solution with small residual norm. By taking one iterate which is resulted by the hybrid SVR-L, putting it as the initial guess, will give us the better solution. To test our idea of prediction of SLEs solutions, we also used the regular regression and compared with the SVR. Numerical results are presented and compared between these two predictors. Lastly, we compared our proposed method with existing interpolation and extrapolation methods to predict the approximate solution of SLEs. The results showed that our restarting SVR-L performed better compared with the regular regression.

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Hosseini, Zeinab Zare, Shekoufeh Kolahdouz Rahimi, Esmaeil Forouzan, and Ahmad Baraani. "RMI-DBG algorithm: A more agile iterative de Bruijn graph algorithm in short read genome assembly." Journal of Bioinformatics and Computational Biology 19, no. 02 (April 2021): 2150005. http://dx.doi.org/10.1142/s0219720021500050.

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The de Bruijn Graph algorithm (DBG) as one of the cornerstones algorithms in short read assembly has extended with the rapid advancement of the Next Generation Sequencing (NGS) technologies and low-cost production of millions of high-quality short reads. Erroneous reads, non-uniform coverage, and genomic repeats are three major problems that influence the performance of short read assemblers. To encounter these problems, the iterative DBG algorithm applies multiple [Formula: see text]-mers instead of a single [Formula: see text]-mer, by iterating the DBG graph over a range of [Formula: see text]-mer sizes from the minimum to the maximum. However, the iteration paradigm of iterative DBG deals with complex graphs from the beginning of the algorithm and therefore, causes more potential errors and computational time for resolving various unreal branches. In this research, we propose the Reverse Modified Iterative DBG graph (named RMI-DBG) for short read assembly. RMI-DBG utilizes the DBG algorithm and String graph to achieve the advantages of both algorithms. We present that RMI-DBG performs faster with comparable results in comparison to iterative DBG. Additionally, the quality of the proposed algorithm in terms of continuity and accuracy is evaluated with some commonly-used assemblers via several real datasets of the GAGE-B benchmark.

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Ésik, Z., and W. Kuich. "Free iterative and iteration K-semialgebras." Algebra universalis 67, no. 2 (March 3, 2012): 141–62. http://dx.doi.org/10.1007/s00012-012-0179-y.

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Keller, Julien. "Ricci iterations on Kähler classes." Journal of the Institute of Mathematics of Jussieu 8, no. 4 (January 30, 2009): 743–68. http://dx.doi.org/10.1017/s1474748009000103.

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AbstractIn this paper we consider the dynamical system involved by the Ricci operator on the space of Kähler metrics of a Fano manifold. Nadel has defined an iteration scheme given by the Ricci operator and asked whether it has some non-trivial periodic points. First, we prove that no such periodic points can exist. We define the inverse of the Ricci operator and consider the dynamical behaviour of its iterates for a Fano Kähler–Einstein manifold. Then we define a finite-dimensional procedure to give an approximation of Kähler–Einstein metrics using this iterative procedure and apply it on ℂℙ2 blown up in three points.

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Wang, Jin-Ping, Jian-Fei Zhang, Zhi-Guo Qu, and Wen-Quan Tao. "An adaptive inner iterative pressure-based algorithm for steady and unsteady incompressible flows." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 4 (April 15, 2019): 2003–24. http://dx.doi.org/10.1108/hff-09-2018-0483.

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Purpose Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are proposed to get efficient solutions. However, the number of inner iterations is set empirically and kept fixed during the whole computation for different problems, which is overestimated in some computations but underestimated in other computations. This paper aims to develop an algorithm with adaptive inner iteration processes for steady and unsteady incompressible flows. Design/methodology/approach In this work, with the use of two different criteria in two inner iterative processes, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary during computing according to different problems. By doing so, adaptive inner iteration processes can be achieved. Findings The adaptive inner iterative algorithm is verified to be valid by solving classic steady and unsteady incompressible problems. Results show that the adaptive inner iteration algorithm works more efficient than the fixed inner iteration one. Originality/value The algorithm with adaptive inner iteration processes is first proposed in this paper. As the mechanism for controlling inner iteration processes is based on physical meaning and the feature of iterative calculations, it can be used in any methods where there exist inner iteration processes. It is not limited for incompressible flows. The performance of the adaptive inner iteration processes in compressible flows is conducted in a further study.

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PLONKA, GERLIND, and JIANWEI MA. "CONVERGENCE OF AN ITERATIVE NONLINEAR SCHEME FOR DENOISING OF PIECEWISE CONSTANT IMAGES." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 06 (November 2007): 975–95. http://dx.doi.org/10.1142/s0219691307002142.

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In this paper we present a new efficient iterative nonlinear scheme for recovering of a piecewise constant image from an observed image containing additive noise. We apply an adaptive neighborhood filter which comes from robust statistics and completely rejects outliers being greater than a certain constant. We prove that the iterated application of the scheme leads to a piecewise constant image. This observation generalizes the known results on convergence of nonlinear diffusion schemes to a constant steady-state. Moreover, we show that the partition of the image determining the piecewise constant steady-state after an infinite iteration process can already be found after a finite number of iteration steps. This result can be used for a fast approximation of the piecewise constant image by a mean value procedure. We examine the relations of our scheme to average and bilateral filtering, diffusion filtering and wavelet shrinkage. Numerical experiments illustrate the performance of the algorithm.

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Yao, Xinwei, Ohad Fried, Kayvon Fatahalian, and Maneesh Agrawala. "Iterative Text-Based Editing of Talking-Heads Using Neural Retargeting." ACM Transactions on Graphics 40, no. 3 (August 2021): 1–14. http://dx.doi.org/10.1145/3449063.

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We present a text-based tool for editing talking-head video that enables an iterative editing workflow. On each iteration users can edit the wording of the speech, further refine mouth motions if necessary to reduce artifacts, and manipulate non-verbal aspects of the performance by inserting mouth gestures (e.g., a smile) or changing the overall performance style (e.g., energetic, mumble). Our tool requires only 2 to 3 minutes of the target actor video and it synthesizes the video for each iteration in about 40 seconds, allowing users to quickly explore many editing possibilities as they iterate. Our approach is based on two key ideas. (1) We develop a fast phoneme search algorithm that can quickly identify phoneme-level subsequences of the source repository video that best match a desired edit. This enables our fast iteration loop. (2) We leverage a large repository of video of a source actor and develop a new self-supervised neural retargeting technique for transferring the mouth motions of the source actor to the target actor. This allows us to work with relatively short target actor videos, making our approach applicable in many real-world editing scenarios. Finally, our, refinement and performance controls give users the ability to further fine-tune the synthesized results.

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Liu, Yi Di. "Research on Iterative Method in Solving Linear Equations on the Hadoop Platform." Applied Mechanics and Materials 347-350 (August 2013): 2763–68. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.2763.

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Solving linear equations is ubiquitous in many engineering problems, and iterative method is an efficient way to solve this question. In this paper, we propose a general iteration method for solving linear equations. Our general iteration method doesnt contain denominators in its iterative formula, and this relaxes the limits that traditional iteration methods require the coefficient aii to be non-zero. Moreover, as there is no division operation, this method is more efficient. We implement this method on the Hadoop platform, and compare it with the Jacobi iteration, the Guass-Seidel iteration and the SOR iteration. Experiments show that our proposed general iteration method is not only more efficient, but also has a good scalability.

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Proinov, Petko D., and Maria T. Vasileva. "A New Family of High-Order Ehrlich-Type Iterative Methods." Mathematics 9, no. 16 (August 5, 2021): 1855. http://dx.doi.org/10.3390/math9161855.

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One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.

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Proinov, Petko D. "Two Classes of Iteration Functions and Q-Convergence of Two Iterative Methods for Polynomial Zeros." Symmetry 13, no. 3 (February 25, 2021): 371. http://dx.doi.org/10.3390/sym13030371.

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In this work, two broad classes of iteration functions in n-dimensional vector spaces are introduced. They are called iteration functions of the first and second kind at a fixed point of the corresponding iteration function. Two general local convergence theorems are presented for Picard-type iterative methods with high Q-order of convergence. In particular, it is shown that if an iterative method is generated by an iteration function of first or second kind, then it is Q-convergent under each initial approximation that is sufficiently close to the fixed point. As an application, a detailed local convergence analysis of two fourth-order iterative methods is provided for finding all zeros of a polynomial simultaneously. The new results improve the previous ones for these methods in several directions.

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Zeng, Huai En. "Iterative and Non-Iterative Solution of Planar Resection." Advanced Materials Research 919-921 (April 2014): 1295–98. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.1295.

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Planar resection is a common surveying work. The paper introduces its frequently-used solution i.e. the iterative solution. However, the iterative solution needs linearization, initial value of parameter and iteration, unfortunately the initial value of parameter is hard to assess in advance, resultantly, the iteration will fail. Due to inexistence of the above problem, the non-iterative solution based on polynomial resultant or Groebner basis and Jacobi algorithm is presented. A numerical case is given to demonstrate the two solutions. It is suggested for the redundant observation cases that the non-iterative solution should be adopted to assess the initial value of parameter, and then the iterative solution should be employed to compute the final result.

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Zhang, Jing Xi. "Optimization of LDPC Coded IDMA System." Applied Mechanics and Materials 148-149 (December 2011): 1066–71. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.1066.

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The issue of optimization of LDPC Coded IDMA system is studied. The iterative decoding process of LDPC code is called inner iteration, and the iterative process between LDPC code and elementary signal estimator (ESE) is called outer iteration. The performance of the system is shown by BER and the complexity is indicated by iteration number. Check matrix is constructed randomly based on the obtained degree profile and simulations are made. The results show that performance of the system improves as the iteration number increases, either inner or outer iteration number. On the other hand, the performance gain of the system decreases with the increase of iteration number. Besides, the performance can be improved by reasonable setting of iteration number with the same complexity.

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Cameron, T. M., and J. H. Griffin. "An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems." Journal of Applied Mechanics 56, no. 1 (March 1, 1989): 149–54. http://dx.doi.org/10.1115/1.3176036.

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A method is proposed for analyzing the steady-state response of nonlinear dynamic systems. The method iterates to obtain the discrete Fourier transform of the system response, returning to the time domain at each iteration to take advantage of the ease in evaluating nonlinearities there—rather than analytically describing the nonlinear terms in the frequency domain. The updated estimates of the nonlinear terms are transformed back into the frequency domain in order to continue iterating on the frequency spectrum of the steady-state response. The method is demonstrated by solving a problem with friction damping in which the excitation has multiple discrete frequencies.

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Ma, Huaifa, Jikai Zhou, and Guoping Liang. "Implicit Damping Iterative Algorithm to Solve Elastoplastic Static and Dynamic Equations." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/486171.

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This paper presents an implicit damping iterative algorithm to simultaneously solve equilibrium equations, yield function, and plastic flow equations, without requiring an explicit expression of elastoplastic stiffness matrices and local iteration for “return mapping” stresses to the yield surface. In addition, a damping factor is introduced to improve the stiffness matrix conformation in the nonlinear iterative process. The incremental iterative scheme and whole amount iterative scheme are derived to solve the dynamical and static and dynamical elastoplastic problems. To validate the proposed algorithms, computation procedures are designed and the numerical tests are implemented. The computational results verify the correctness and reliability of the proposed implicit iteration algorithms.

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Moore, Kevin L., Hyo-Sung Ahn, and Yang Quan Chen. "Iteration domainH∞-optimal iterative learning controller design." International Journal of Robust and Nonlinear Control 18, no. 10 (2008): 1001–17. http://dx.doi.org/10.1002/rnc.1231.

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Li, Xu, Yu-Jiang Wu, Ai-Li Yang, and Jin-Yun Yuan. "A Generalized HSS Iteration Method for Continuous Sylvester Equations." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/578102.

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Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the iterative process. An exact parameter region of convergence for the method is strictly proved and a minimum value for the upper bound of the iterative spectrum is derived. Moreover, to reduce the computational cost, we establish an inexact variant of the GHSS (IGHSS) iteration method whose convergence property is discussed. Numerical experiments illustrate the efficiency and robustness of the GHSS iteration method and its inexact variant.

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Zhang, Yanmei, Xia Cui, and Guangwei Yuan. "Nonlinear iteration acceleration solution for equilibrium radiation diffusion equation." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 5 (June 26, 2020): 1465–90. http://dx.doi.org/10.1051/m2an/2019095.

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This paper discusses accelerating iterative methods for solving the fully implicit (FI) scheme of equilibrium radiation diffusion problem. Together with the FI Picard factorization (PF) iteration method, three new nonlinear iterative methods, namely, the FI Picard-Newton factorization (PNF), FI Picard-Newton (PN) and derivative free Picard-Newton factorization (DFPNF) iteration methods are studied, in which the resulting linear equations can preserve the parabolic feature of the original PDE. By using the induction reasoning technique to deal with the strong nonlinearity of the problem, rigorous theoretical analysis is performed on the fundamental properties of the four iteration methods. It shows that they all have first-order time and second-order space convergence, and moreover, can preserve the positivity of solutions. It is also proved that the iterative sequences of the PF iteration method and the three Newton-type iteration methods converge to the solution of the FI scheme with a linear and a quadratic speed respectively. Numerical tests are presented to confirm the theoretical results and highlight the high performance of these Newton acceleration methods.

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Hong, Baojian, and Dianchen Lu. "Modified Fractional Variational Iteration Method for Solving the Generalized Time-Space Fractional Schrödinger Equation." Scientific World Journal 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/964643.

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Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.

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Sukarna, S., Muhammad Abdy, and R. Rahmat. "Perbandingan Metode Iterasi Jacobi dan Metode Iterasi Gauss-Seidel dalam Menyelesaikan Sistem Persamaan Linear Fuzzy." Journal of Mathematics, Computations, and Statistics 2, no. 1 (May 12, 2020): 1. http://dx.doi.org/10.35580/jmathcos.v2i1.12447.

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Penelitian ini mengkaji tentang menyelesaian Sistem Persamaan Linear Fuzzy dengan Membanding kan Metode Iterasi Jacobi dan Metode Iterasi Gauss-Seidel. Metode iterasi Jacobi merupakan salah satu metode tak langsung, yang bermula dari suatu hampiran Metode iterasi Jacobi ini digunakan untuk menyelesaikan persamaan linier yang proporsi koefisien nol nya besar. Iterasi dapat diartikan sebagai suatu proses atau metode yang digunakan secara berulang-ulang (pengulangan) dalam menyelesaikan suatu permasalahan matematika ditulis dalam bentuk . Pada metode iterasi Gauss-Seidel, nilai-nilai yang paling akhir dihitung digunakan di dalam semua perhitungan. Jelasnya, di dalam iterasi Jacobi, menghitung dalam bentuk . Setelah mendapatkan Hasil iterasi kedua Metode tersebut maka langkah selanjutnya membandingkan kedua metode tersebut dengan melihat jumlah iterasinya dan nilai Galatnya manakah yang lebih baik dalam menyelesaikan Sistem Persamaan Linear Fuzzy.Kata kunci: Sistem Persamaan Linear Fuzzy, Metode Itersi Jacobi, Metode Iterasi Gauss-Seidel. This study examines the completion of the Linear Fuzzy Equation System by Comparing the Jacobi Iteration Method and the Gauss-Seidel Iteration Method. The Jacobi iteration method is one of the indirect methods, which stems from an almost a method of this Jacobi iteration method used to solve linear equations whose proportion of large zero coefficients. Iteration can be interpreted as a process or method used repeatedly (repetition) in solving a mathematical problem written in the form . In the Gauss-Seidel iteration method, the most recently calculated values are used in all calculations. Obviously, inside Jacobi iteration, counting in form After obtaining the result of second iteration of the Method then the next step compare both methods by seeing the number of iteration and the Error value which is better in solving Linear Fuzzy Equation System.Keywords: Linear Fuzzy Equation System, Jacobi Itersi Method, Gauss-Seidel Iteration Method.

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Castaño, F., L. Laín, M. N. Sanchez, and A. Torre. "A general iterative time-independent perturbation theory." Canadian Journal of Physics 63, no. 9 (September 1, 1985): 1157–61. http://dx.doi.org/10.1139/p85-189.

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An iterative method for time-independent perturbation theory is presented. Lennard-Jones–Brillouin–Wigner (LBW) and Rayleigh–Schrödinger (RS) power series are shown to be particular cases of the iteration and the combined expansion–iteration. Improvements in convergence of the power series are suggested and analyzed.The iterative method gives considerable insight into the nature and relative convergence of the currently used time-independent perturbation methods.

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Chen, Huijuan, and Xintao Zheng. "Improved Newton Iterative Algorithm for Fractal Art Graphic Design." Complexity 2020 (November 27, 2020): 1–11. http://dx.doi.org/10.1155/2020/6623049.

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Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. The selection of the initial value of the first iteration has a greater impact on the final calculation result. If the initial value of the iteration is not selected properly, the iteration will not converge or will converge to the wrong result, which will affect the accuracy of the fractal art graphic design. Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. Through the area division method of the system composed of the sensor array, the effective initial value of iterative calculation is selected in the corresponding area for subsequent iterative calculation. Using the special skeleton structure of Newton’s iterative graphics, such as infinitely finely inlaid chain-like, scattered-point-like composition, combined with the use of graphic secondary design methods, we conduct fractal art graphics design research with special texture effects. On this basis, the Newton iterative graphics are processed by dithering and MATLAB-based mathematical morphology to obtain graphics and then processed with the help of weaving CAD to directly form fractal art graphics with special texture effects. Design experiments with the help of electronic Jacquard machines proved that it is feasible to transform special texture effects based on Newton's iterative graphic design into Jacquard fractal art graphics.

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Lin, R. F., H. M. Ren, Z. Šmarda, Q. B. Wu, Y. Khan, and J. L. Hu. "New Families of Third-Order Iterative Methods for Finding Multiple Roots." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/812072.

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Two families of third-order iterative methods for finding multiple roots of nonlinear equations are developed in this paper. Mild conditions are given to assure the cubic convergence of two iteration schemes (I) and (II). The presented families include many third-order methods for finding multiple roots, such as the known Dong's methods and Neta's method. Some new concrete iterative methods are provided. Each member of the two families requires two evaluations of the function and one of its first derivative per iteration. All these methods require the knowledge of the multiplicity. The obtained methods are also compared in their performance with various other iteration methods via numerical examples, and it is observed that these have better performance than the modified Newton method, and demonstrate at least equal performance to iterative methods of the same order.

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Thukral, R. "Introduction to a family of Thukral k-order method for finding multiple zeros of nonlinear equations." JOURNAL OF ADVANCES IN MATHEMATICS 13, no. 3 (June 15, 2017): 7230–37. http://dx.doi.org/10.24297/jam.v13i3.6146.

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A new one-point k-order iterative method for finding zeros of nonlinear equations having unknown multiplicity is introduced. In terms of computational cost the new iterative method requires k+1 evaluations of functions per iteration. It is shown that the new iterative method has a convergence of order k.

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41

Liu, Zhongyun, Xiaorong Qin, Nianci Wu, and Yulin Zhang. "The Shifted Classical Circulant and Skew Circulant Splitting Iterative Methods for Toeplitz Matrices." Canadian Mathematical Bulletin 60, no. 4 (December 1, 2017): 807–15. http://dx.doi.org/10.4153/cmb-2016-077-5.

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AbstractIt is known that every Toeplitz matrix T enjoys a circulant and skew circulant splitting (denoted CSCS) i.e., T = C−S with C a circulantmatrix and S a skew circulantmatrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive deûnite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss–Seidel (GS) iterative methods if the CSCS is convergent, and that there is always a constant α such that the shifted CSCS iteration converges much faster than the Gauss–Seidel iteration, no matter whether the CSCS itself is convergent or not.

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42

Endaryono, Endaryono. "Karakteristik Komputasi Penentuan Akar Kuadrat Bilangan Nonkuadrat Sempurna Beberapa Metode Iteratif Menggunakan Pemograman QBasic." Jurnal Ilmu Pendidikan (JIP) STKIP Kusuma Negara 11, no. 2 (January 10, 2020): 76–87. http://dx.doi.org/10.37640/jip.v11i2.92.

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Penyelesaian beberapa masalah matematika tidak hanya menggunakan metode analitik tetapi juga dengan metode numerik yang prosesnya iteratif. Dalam metode numerik, selain mahasiswa memahami perhitungan tiap iterasi secara manual juga perlu untuk memahami penyelesaian menggunakan coding atau pemograman. Satu diantara program yang mudah diunduh adalah QBasic. Tulisan ini membahas penentuan akar bilangan bulat yang bukan bilangan kuadrat sempurna yaitu akar kuadrat dari 3 menggunakan metode numerik dengan teknik iteratif. Tujuan penulisan adalah melihat karakteristik komputasi dalam jumlah iterasi pada metode Heron, bagi dua, posisi palsu, dan Newton Raphson. Penelitian melalui simulasi menggunakan pemgroman QBasic. Nilai kesalahan (eror) dalam simulasi pada metode yang dilakukan ditetapkan pada nilai 1x10-10 atau iterasi masih akan jika nlai kesalahan lebih dari nilai kesalahan yang ditetapkan. Hasil simulasi didapatkan bahwa pada nilai kesalahan tersebut nilai akar kuadrat bilangan 3 berkisar pada 1,73205. Metode Heron dan metode Newton Raphson memiliki jumlah iterasi yang sama, yaitu 6 iterasi, relatif lebih sedikit dibandingkan metode iteratif lain. Kesimpulan penelitian adalah pada penentuan akar kudrat dari bilangan 3 metode Heron dan metode Newton Raphson memberikan kinerja komputasi yang lebih baik dari jumlah iterasi dibanding pada metode bagi dua dan metode posisi palsu.

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Li, Yazhe, Kai Zhou, and Zhen Zhang. "The flow-difference feedback iteration method for aerostatic thrust bearings and its convergence characteristics." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 233, no. 11 (April 29, 2019): 1743–52. http://dx.doi.org/10.1177/1350650119846230.

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The flow-difference feedback iteration method for aerostatic thrust bearings is proposed to the flow balance-based iteration, and two modification methods are further provided to improve the adaptability. The bearing capability calculated by the proposed method is validated by the experimental data. Moreover, the influence of convergence rate factors, iterative initial values, and mesh grids on the iteration ratio is investigated. Compared with the conventional iteration methods, the proposed method with appropriate convergence rate factors provides a higher convergence efficiency. In addition, good convergence behavior under different iterative initial values and the mesh grid size is shown, and the convergence rate is insensitive to the finite difference method parameters. A series of calculations are conducted to investigate the generality of the proposed methods.

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Li, Xia, Zhanqiang Song, Guiping Shen, Ying Huang, and Junyu Chen. "Diagnostic Value of Chest CT Images Based on Full Model Iterative Reconstruction Algorithm for Lung Cancer Patients." Scientific Programming 2021 (September 10, 2021): 1–7. http://dx.doi.org/10.1155/2021/5257682.

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Objective. To evaluate the value of low-dose CT scanning and full model iteration recombinant technology peripheral lung cancer in the paper using whole model iterative reconstruction algorithm and compare iterative model-wide restructuring, reorganization part of an iterative algorithm, affecting filtered back projection image quality. Method. Fifty-two patients with peripheral lung cancer, all of whom were diagnosed by pathological biopsy, were selected for the study. All patients received three scans of low-dose chest CT, next-low-dose, and low-dose, after which the raw data of three different doses were reconstructed using filtered back-projection, iterative partial algorithm reconstitution, and reconstructed full-model iteration, respectively, and the effect of each algorithm on the processing of chest CT images of peripheral lung cancer at different doses and the diagnosis of the disease were compared after the reconstitution was completed. Results. The average effective radiation dose for the low-dose group was (0.3±0.02) mSv At each dose level, image noise objective recombinant whole iterative model < part of the reorganization of the iterative algorithm < filtered back projection, the difference was significant. In the case of lung lesions, the full-model iterative algorithm has similar evaluation power to the LD-partial iterative algorithm. When a patient’s body mass index (BMI) > 25 kg/m2, the whole model iteration reorganization image quality is reduced, but the lesions-to-noise ratio (SNR) is unaffected. Conclusion. The combination of a very low dose of recombinant iterative model as compared to full-dose low-dose chest CT dose can be reduced to 88% but does not reduce the overall image quality and can show good radiological signs of peripheral lung cancer and not affect BMI patients.

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Xu, Qiuyan, and Zhiyong Liu. "Alternating Asymmetric Iterative Algorithm Based on Domain Decomposition for 3D Poisson Problem." Mathematics 8, no. 2 (February 19, 2020): 281. http://dx.doi.org/10.3390/math8020281.

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Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several sub-domains, and eight asymmetric iterative schemes with the relaxation factor for 3D Poisson equation are constructed. When the numbers of iteration are odd or even, the computational process of the presented iterative algorithm are proposed respectively. In the calculation of the inner interfaces, the group explicit method is used, which makes the algorithm to be performed fast and in parallel, and avoids the difficulty of solving large-scale linear equations. Furthermore, the convergence of the algorithm is analyzed theoretically. Finally, by comparing with the numerical experimental results of Jacobi and Gauss Seidel iterative algorithms, it is shown that the alternating asymmetric iterative algorithm based on domain decomposition has shorter computation time, fewer iteration numbers and good parallelism.

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Zeng, Xiaoniu, Xihai Li, Juan Su, Daizhi Liu, and Hongxing Zou. "An adaptive iterative method for downward continuation of potential-field data from a horizontal plane." GEOPHYSICS 78, no. 4 (July 1, 2013): J43—J52. http://dx.doi.org/10.1190/geo2012-0404.1.

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We have developed an improved adaptive iterative method based on the nonstationary iterative Tikhonov regularization method for performing a downward continuation of the potential-field data from a horizontal plane. Our method uses the Tikhonov regularization result as initial value and has an incremental geometric choice of the regularization parameter. We compared our method with previous methods (Tikhonov regularization, Landweber iteration, and integral-iteration method). The downward-continuation performance of these methods in spatial and wavenumber domains were compared with the aspects of their iterative schemes, filter functions, and downward-continuation operators. Applications to synthetic gravity and real aeromagnetic data showed that our iterative method yields a better downward continuation of the data than other methods. Our method shows fast computation times and a stable convergence. In addition, the [Formula: see text]-curve criterion for choosing the regularization parameter is expressed here in the wavenumber domain and used to speed up computations and to adapt the wavenumber-domain iterative method.

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Tian, Qihua, Yurong Zhang, Qunmei Dong, Xiangman Zhou, and Yixian Du. "Research on multi-stage iterative model solving method with resource optimization configuration." MATEC Web of Conferences 309 (2020): 05014. http://dx.doi.org/10.1051/matecconf/202030905014.

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Aiming at the problem of unreasonable resource allocation in the existing coupling design iterative model based on efficiency constraint, the resource equilibrium strategy was introduced into the iterative model. In order to reduce the time cost of product development, a multi-stage iterative model with optimal resource allocation was constructed and the optimal resource allocation of each task group was obtained by solving this model. Taking the design and development process of an air purifier as an example, the validity of this model was verified. The research shows that after introducing resource equilibrium strategy into the iterative model based on efficiency constraint, the time cost of iterative mode in different stages decreases, and with the increase of the number of iteration stages, the time cost decreases first and then increases. The research results provide a theoretical basis for designers to reasonably select resource allocation mode and number of iteration stages in actual product development so as to optimize resource allocation and reduce development cost.

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Wang, Shou Jun, and Ming Wei Wei. "Application of Accelerated Iterative Method in Calculating Wave Length in Harbor Engineering." Applied Mechanics and Materials 130-134 (October 2011): 3481–84. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.3481.

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In this paper, a specific application accelerated iterative method is presented for calculating wave length in harbor engineering, which includes calculation method of wave length and specific implement in Excel. Different wavelengths into the iteration formula to calculate the same result can be obtained, but the calculation speed of different methods have significant differences to arrive at the fastest method . Calculated by accelerating the iteration method can significantly increase the computing speed and calculation steps. After the derivation of several methods and calculations show that Newton iteration is the fastest way to convergence speed, in the practical range of about 10 steps through the iterative convergence results can be obtained.

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Ben-Romdhane, Mohamed, and Helmi Temimi. "An Iterative Numerical Method for Solving the Lane–Emden Initial and Boundary Value Problems." International Journal of Computational Methods 15, no. 04 (May 24, 2018): 1850020. http://dx.doi.org/10.1142/s0219876218500202.

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In this paper, we propose fast iterative methods based on the Newton–Raphson–Kantorovich approximation in function space [Bellman and Kalaba, (1965)] to solve three kinds of the Lane–Emden type problems. First, a reformulation of the problem is performed using a quasilinearization technique which leads to an iterative scheme. Such scheme consists in an ordinary differential equation that uses the approximate solution from the previous iteration to yield the unknown solution of the current iteration. At every iteration, a further discretization of the problem is achieved which provides the numerical solution with low computational cost. Numerical simulation shows the accuracy as well as the efficiency of the method.

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Zafar, Fiza, Nusrat Yasmin, Saima Akram, and Moin-ud-Din Junjua. "A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation." Scientific World Journal 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/934260.

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We construct a new general class of derivative freen-point iterative methods of optimal order of convergence2n-1using rational interpolant. The special cases of this class are obtained. These methods do not need Newton’s iterate in the first step of their iterative schemes. Numerical computations are presented to show that the new methods are efficient and can be seen as better alternates.

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Journal articles on the topic 'Iteratie'

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