Relevant bibliographies by topics / Iteration methods

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Iteration methods'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 May 2022

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Journal articles on the topic "Iteration methods"

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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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de Lima, Camila, and Elias Salomão Helou. "Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction." Journal of Synchrotron Radiation 25, no. 1 (January 1, 2018): 248–56. http://dx.doi.org/10.1107/s1600577517015715.

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Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughlyO(N3) floating point operations (flops) forN×Npixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator toO(N2logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost ofO(N2logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.
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Rehman, Habib ur, Poom Kumam, Ioannis K. Argyros, Nasser Aedh Alreshidi, Wiyada Kumam, and Wachirapong Jirakitpuwapat. "A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems." Symmetry 12, no. 4 (April 2, 2020): 523. http://dx.doi.org/10.3390/sym12040523.

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The main objective of this article is to propose a new method that would extend Popov’s extragradient method by changing two natural projections with two convex optimization problems. We also show the weak convergence of our designed method by taking mild assumptions on a cost bifunction. The method is evaluating only one value of the bifunction per iteration and it is uses an explicit formula for identifying the appropriate stepsize parameter for each iteration. The variable stepsize is going to be effective for enhancing iterative algorithm performance. The variable stepsize is updating for each iteration based on the previous iterations. After numerical examples, we conclude that the effect of the inertial term and variable stepsize has a significant improvement over the processing time and number of iterations.
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Papadrakakis, M. "Accelerating Vector Iteration Methods." Journal of Applied Mechanics 53, no. 2 (June 1, 1986): 291–97. http://dx.doi.org/10.1115/1.3171754.

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This paper describes a technique for accelerating the convergence properties of iterative methods for the solution of large sparse symmetric linear systems that arise from the application of finite element method. The technique is called partial preconditioning process (PPR) and can be combined with pure vector iteration methods, such as the conjugate gradient, the dynamic relaxation, and the Chebyshev semi-iterative methods. The proposed triangular splitting preconditioner combines Evans’ SSOR preconditioner with a drop-off tolerance criterion. The (PPR) is attractive in a FE framework because it is simple and can be implemented at the element level as opposed to incomplete Cholesky preconditioners, which require a sparse assembly. The method, despite its simplicity, is shown to be more efficient on a set of test problems for certain values of the drop-off tolerance parameter than the partial elimination method.
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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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Al-Mohssen, Husain A., Nicolas G. Hadjiconstantinou, and Ioannis G. Kevrekidis. "Acceleration Methods for Coarse-Grained Numerical Solution of the Boltzmann Equation." Journal of Fluids Engineering 129, no. 7 (December 4, 2006): 908–12. http://dx.doi.org/10.1115/1.2742725.

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We present a coarse-grained steady-state solution framework for the Boltzmann kinetic equation based on a Newton-Broyden iteration. This approach is an extension of the equation-free framework proposed by Kevrekidis and coworkers, whose objective is the use of fine-scale simulation tools to directly extract coarse-grained, macroscopic information. Our current objective is the development of efficient simulation tools for modeling complex micro- and nanoscale flows. The iterative method proposed and used here consists of a short Boltzmann transient evolution step and a Newton-Broyden contraction mapping step based on the Boltzmann solution; the latter step only solves for the macroscopic field of interest (e.g., flow velocity). The predicted macroscopic field is then used as an initial condition for the Boltzmann solver for the next iteration. We have validated this approach for isothermal, one-dimensional flows in the low Knudsen number regime. We find that the Newton-Broyden iteration converges in O(10) iterations, starting from arbitrary guess solutions and a Navier-Stokes based initial Jacobian. This results in computational savings compared to time-explicit integration to steady states when the time to steady state is longer than O(40) mean collision times.
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Mat Ali, Nur Afza, Jumat Sulaiman, Azali Saudi, and Nor Syahida Mohamad. "Performance of similarity explicit group iteration for solving 2D unsteady convection-diffusion equation." Indonesian Journal of Electrical Engineering and Computer Science 23, no. 1 (July 1, 2021): 471. http://dx.doi.org/10.11591/ijeecs.v23.i1.pp471-478.

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In this paper, a similarity finite difference (SFD) solution is addressed for thetwo-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization schemeto get the second-order SFD approximation equation. We propose a four-point similarity explicit group (4-point SEG) iterative methodasa numericalsolution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To showthe 4-point SEG iteration efficiency, two iterative methods, such as Jacobiand Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's performance. Finally, the numerical results showed that our proposed iterative method is more efficient than the Jacobiand GS iterations in terms of iteration number and execution time.
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Zhou, Ting, and Shi Guang Zhang. "Comparison Results between Jacobi and USSOR Iterative Methods." Advanced Materials Research 989-994 (July 2014): 1790–93. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.1790.

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In this paper, some comparison results between Jacobi and USSOR iteration for solving nonsingular linear systems are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of USSOR iterative matrix under some conditions. A numerical example is also given to illustrate our results.
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Gdawiec, Krzysztof, Wiesław Kotarski, and Agnieszka Lisowska. "Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods." Abstract and Applied Analysis 2015 (2015): 1–19. http://dx.doi.org/10.1155/2015/797594.

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A survey of some modifications based on the classic Newton’s and the higher order Newton-like root finding methods for complex polynomials is presented. Instead of the standard Picard’s iteration several different iteration processes, described in the literature, which we call nonstandard ones, are used. Kalantari’s visualizations of root finding process are interesting from at least three points of view: scientific, educational, and artistic. By combining different kinds of iterations, different convergence tests, and different colouring we obtain a great variety of polynomiographs. We also check experimentally that using complex parameters instead of real ones in multiparameter iterations do not destabilize the iteration process. Moreover, we obtain nice looking polynomiographs that are interesting from the artistic point of view. Real parts of the parameters alter symmetry, whereas imaginary ones cause asymmetric twisting of polynomiographs.
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Pour, H. Noormohammadi, and H. Sadeghi Goughery. "Generalized Accelerated Hermitian and Skew-Hermitian Splitting Methods for Saddle-Point Problems." Numerical Mathematics: Theory, Methods and Applications 10, no. 1 (February 2017): 167–85. http://dx.doi.org/10.4208/nmtma.2017.m1524.

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AbstractWe generalize the accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solution of the saddle-point problem. Numerical experiments are used to further examine the effectiveness and robustness of iterations.
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Dissertations / Theses on the topic "Iteration methods"

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Nikazad, Touraj. "Algebraic Reconstruction Methods." Doctoral thesis, Linköping : Linköpings universitet, Department of Mathematics Scientific Computing, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11670.

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Mohammadpour, Rahman. "New methods in forcing iteration and applications." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7050.

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Dans cette thèse on considère l’itération de forcing en utilisant des modèles virtuels comme conditions latérales. Le but ultime de ces techniques est de trouver un axiome de forcing supérieur. Dans le premier chapitre, nous présentons les matériaux nécessaires, y compris les définitions et les lemmes pour les chapitres suivants. Le deuxième chapitre contient quelques constructions avec des conditions latérales appelées scaffolding poset; c’est un échauffement pour les constructions compliquées des chapitres suivants. La notion de modèle virtuel et ses propriétés sont introduites et étudiées en détail dans le troisième chapitre, où nous étudions également la manière dont les modèles virtuels de différents types interagissent. Nous introduisons ensuite dans le chapitre quatre la notion de forcing qui consiste à les conditions latérales pures qui sont des ensembles finis de modèles dénombrables et de modèles Magidor. Dans le chapitre cinq, nous avons intégré des forcings dans la construction du chapitre quatre pour former une itération, nous analysons les propriétés de l’itération et de ses quotients par des modèle Magidors, par exemple la propriété de ω1-approximation. L’itération donne en effet un axiome de forcing pour une certaine classe de forcings propres qui est compatible avec 2ℵ0 > @2. Le dernier chapitre est consacré à l’étude des modèles d’estimation, nous introduisons certains principes combinatoires en termes de modèles de devinettes qui peuvent être considérés comme les conséquences d’un axiome de forcing supérieur. Nous montrons leur cohérence et énonçons leurs conséquences concernant l’idéal des points approchables, le principe de maximalité d’Abraham etc
This thesis concerns forcing iterations using virtual models as side conditions. The ultimate goal of such techniques is to achieve a higher forcing axiom. In the firstchapter, we present the necessary materials, including definitions and lemmata for the later chapters. The chapter two contains the scaffolding poset which is a warmup for the later constructions. The notion of a virtual model and its properties are introduced and investigated extensively in the third chapter, where we also study how the virtual models of different types interact. We then introduce, in the fourth chapter, the forcing notion consisting of pure side conditions which are finite sets of countable virtual models and Magidor models. In the chapter five, we plug forcings in our construction from the fourth chapter to form an iteration using virtual models, we analyze properties of our iteration and its quotients by Magidor models suchas the ω1-approximation. The iteration indeed gives a forcing axiom for a certain class of proper forcings which is compatible with 2ℵ0 > @2. The chapter six is devotedto the study of guessing models and their specialization, we introduce certain combinatorial principles in terms of guessing models which can be considered as consequencesof a higher forcing axiom. We shall show their consistency and state their consequences concerning the approachability ideal, Abraham’s maximality principle etc
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Garner, William Howard. "Iteration of the power operation." Virtual Press, 1995. http://liblink.bsu.edu/uhtbin/catkey/941367.

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This thesis is an investigation of the sequence of functions defined by fl (x) -xand fn+1 (x) -x , where the power is the principal value.In the case where the sequence is restricted to positive real this sequence of functions over thecomplex plane, we attack real numbers, the problem yields to the methods of analysis and we prove the behavior of the sequence.The more general problem of describing the behavior of both analytically and numerically. Though no full rigorous solution is given, the results presented suggest the behavior of the sequence over the complex plane is very interesting.
Department of Mathematical Sciences
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Vogelgesang, Jonas [Verfasser]. "Semi-discrete iteration methods in x-ray tomography / Jonas Vogelgesang." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2020. http://d-nb.info/1219068713/34.

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Freitag, Melina. "Inner-outer iterative methods for eigenvalue problems : convergence and preconditioning." Thesis, University of Bath, 2007. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.512248.

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Many methods for computing eigenvalues of a large sparse matrix involve shift-invert transformations which require the solution of a shifted linear system at each step. This thesis deals with shift-invert iterative techniques for solving eigenvalue problems where the arising linear systems are solved inexactly using a second iterative technique. This approach leads to an inner-outer type algorithm. We provide convergence results for the outer iterative eigenvalue computation as well as techniques for efficient inner solves. In particular eigenvalue computations using inexact inverse iteration, the Jacobi-Davidson method without subspace expansion and the shift-invert Arnoldi method as a subspace method are investigated in detail. A general convergence result for inexact inverse iteration for the non-Hermitian generalised eigenvalue problem is given, using only minimal assumptions. This convergence result is obtained in two different ways; on the one hand, we use an equivalence result between inexact inverse iteration applied to the generalised eigenproblem and modified Newton's method; on the other hand, a splitting method is used which generalises the idea of orthogonal decomposition. Both approaches also include an analysis for the convergence theory of a version of inexact Jacobi-Davidson method, where equivalences between Newton's method, inverse iteration and the Jacobi-Davidson method are exploited. To improve the efficiency of the inner iterative solves we introduce a new tuning strategy which can be applied to any standard preconditioner. We give a detailed analysis on this new preconditioning idea and show how the number of iterations for the inner iterative method and hence the total number of iterations can be reduced significantly by the application of this tuning strategy. The analysis of the tuned preconditioner is carried out for both Hermitian and non-Hermitian eigenproblems. We show how the preconditioner can be implemented efficiently and illustrate its performance using various numerical examples. An equivalence result between the preconditioned simplified Jacobi-Davidson method and inexact inverse iteration with the tuned preconditioner is given. Finally, we discuss the shift-invert Arnoldi method both in the standard and restarted fashion. First, existing relaxation strategies for the outer iterative solves are extended to implicitly restarted Arnoldi's method. Second, we apply the idea of tuning the preconditioner to the inner iterative solve. As for inexact inverse iteration the tuned preconditioner for inexact Arnoldi's method is shown to provide significant savings in the number of inner solves. The theory in this thesis is supported by many numerical examples.
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Safoutin, Michael John. "A methodology for empirical measurement of iteration in engineering design processes /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/7111.

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Scheben, Fynn. "Iterative methods for criticality computations in neutron transport theory." Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319.

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This thesis studies the so-called “criticality problem”, an important generalised eigenvalue problem arising in neutron transport theory. The smallest positive real eigenvalue of the problem contains valuable information about the status of the fission chain reaction in the nuclear reactor (i.e. the criticality of the reactor), and thus plays an important role in the design and safety of nuclear power stations. Because of the practical importance, efficient numerical methods to solve the criticality problem are needed, and these are the focus of this thesis. In the theory we consider the time-independent neutron transport equation in the monoenergetic homogeneous case with isotropic scattering and vacuum boundary conditions. This is an unsymmetric integro-differential equation in 5 independent variables, modelling transport, scattering, and fission, where the dependent variable is the neutron angular flux. We show that, before discretisation, the nonsymmetric eigenproblem for the angular flux is equivalent to a related eigenproblem for the scalar flux, involving a symmetric positive definite weakly singular integral operator(in space only). Furthermore, we prove the existence of a simple smallest positive real eigenvalue with a corresponding eigenfunction that is strictly positive in the interior of the reactor. We discuss approaches to discretise the problem and present discretisations that preserve the underlying symmetry in the finite dimensional form. The thesis then describes methods for computing the criticality in nuclear reactors, i.e. the smallest positive real eigenvalue, which are applicable for quite general geometries and physics. In engineering practice the criticality problem is often solved iteratively, using some variant of the inverse power method. Because of the high dimension, matrix representations for the operators are often not available and the inner solves needed for the eigenvalue iteration are implemented by matrix-free inneriterations. This leads to inexact iterative methods for criticality computations, for which there appears to be no rigorous convergence theory. The fact that, under appropriate assumptions, the integro-differential eigenvalue problem possesses an underlying symmetry (in a space of reduced dimension) allows us to perform a systematic convergence analysis for inexact inverse iteration and related methods. In particular, this theory provides rather precise criteria on how accurate the inner solves need to be in order for the whole iterative method to converge. The theory is illustrated with numerical examples on several test problems of physical relevance, using GMRES as the inner solver. We also illustrate the use of Monte Carlo methods for the solution of neutron transport source problems as well as for the criticality problem. Links between the steps in the Monte Carlo process and the underlying mathematics are emphasised and numerical examples are given. Finally, we introduce an iterative scheme (the so-called “method of perturbation”) that is based on computing the difference between the solution of the problem of interest and the known solution of a base problem. This situation is very common in the design stages for nuclear reactors when different materials are tested, or the material properties change due to the burn-up of fissile material. We explore the relation ofthe method of perturbation to some variants of inverse iteration, which allows us to give convergence results for the method of perturbation. The theory shows that the method is guaranteed to converge if the perturbations are not too large and the inner problems are solved with sufficiently small tolerances. This helps to explain the divergence of the method of perturbation in some situations which we give numerical examples of. We also identify situations, and present examples, in which the method of perturbation achieves the same convergence rate as standard shifted inverse iteration. Throughout the thesis further numerical results are provided to support the theory.
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Chidume, Chukwudi Soares de Souza Geraldo. "Iteration methods for approximation of solutions of nonlinear equations in Banach spaces." Auburn, Ala., 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SUMMER/Mathematics_and_Statistics/Dissertation/Chidume_Chukwudi_33.pdf.

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Chand, Manoj. "Development of Efficient Numerical Methods for Solving Differential Equations using He's Variational Iteration Technique." Thesis, University of Louisiana at Lafayette, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1553885.

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Differential equations play a prominent role in engineering and research fields in modeling engineering structures, describing important phenomena, and simulating mathematical behavior of engineering dynamical systems. Because of the increasing complexity of modern engineering systems, computationally efficient methods are demanded for solving these differential equations. In order to meet this challenge, this thesis presents two efficient algorithms for solving two types of differential equations: a one-dimensional heat equation with variable properties, and a one-dimensional parabolic equation, both of which are very popular and important in current engineering systems. In this study, the two equations were successfully solved using He’s variational iteration technique, and efficient algorithms have been developed. Detailed procedures for developing these algorithms are presented.

At first, a unique algorithm for solving the one-dimensional heat equations was developed by using the iteration variational approach. The accuracy of this algorithm was found by comparing the obtained solutions with the exact ones.

And similarly, using variational iteration approach, another efficient algorithm for solving the one-dimensional parabolic equation was developed. Three illustrative numerical problems were solved and the obtained results were compared with those yielded from the Adomian decomposition method (ADM) to verify the efficiency and accuracy of the developed algorithm.

With the encouraging results obtained from this study, it is expected that, in the future, developed algorithms can be extended to solve other differential equation systems, thus achieving a broader applicability in engineering and other research fields.

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Lohaka, Hippolyte O. "MAKING A GROUPED-DATA FREQUENCY TABLE: DEVELOPMENT AND EXAMINATION OF THE ITERATION ALGORITHM." Ohio : Ohio University, 2007. http://www.ohiolink.edu/etd/view.cgi?ohiou1194981215.

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Books on the topic "Iteration methods"

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1951-, Ésik Zoltán, ed. Iteration theories: The equational logic of iterative processes. Berlin: Springer-Verlag, 1993.

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Johnston, Catherine M. Simultaneous iteration methods for the eigenproblem. [s.l: The Author], 1992.

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Kelly, Lynne. Mathematics by computer: Iteration. Ballarat, Australia: Wizard Books, 1996.

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Steinmetz, Norbert. Rational iteration: Complex analyticdynamical systems. Berlin: W. de Gruyter, 1993.

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Ferenc, Szidarovszky, ed. The theory and applications of iteration methods. Boca Raton, Fla: CRC Press, 1993.

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Steinmetz, Norbert. Rational iteration: Complex analytic dynamical systems. Berlin: W. de Gruyter, 1993.

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Gilyazov, S. F. Regularization of Ill-Posed Problems by Iteration Methods. Dordrecht: Springer Netherlands, 2000.

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Gili︠a︡zov, S. F. Regularization of ill-posed problems by iteration methods. Doordrecht: Kluwer Academic Publishers, 2000.

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Polynomial based iteration methods for symmetric linear systems. Chichester: Wiley, 1996.

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Bernd, Fischer. Polynomial based iteration methods for symmetric linear systems. Philadelphia: Society for Industrial and Applied Mathematics, 2011.

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Book chapters on the topic "Iteration methods"

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Hong, Sung-Min, Anh-Tuan Pham, and Christoph Jungemann. "Iteration Methods." In Computational Microelectronics, 177–82. Vienna: Springer Vienna, 2011. http://dx.doi.org/10.1007/978-3-7091-0778-2_11.

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Kythe, Prem K., and Pratap Puri. "Iteration Methods." In Computational Methods for Linear Integral Equations, 146–74. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0101-4_6.

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Khoury, Richard, and Douglas Wilhelm Harder. "Iteration." In Numerical Methods and Modelling for Engineering, 31–38. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-21176-3_3.

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Belomestny, Denis, and John Schoenmakers. "Stochastic Policy Iteration Methods." In Advanced Simulation-Based Methods for Optimal Stopping and Control, 97–134. London: Palgrave Macmillan UK, 2018. http://dx.doi.org/10.1057/978-1-137-03351-2_7.

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Hackbusch, Wolfgang. "Nested Iteration Technique." In Multi-Grid Methods and Applications, 98–111. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02427-0_5.

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Hackbusch, Wolfgang. "General Multi-Grid Iteration." In Multi-Grid Methods and Applications, 80–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02427-0_4.

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Angell, Thomas S., Ralph E. Kleinman, and Gary F. Roach. "Iteration Methods for Potential Problems." In Potential Theory, 13–28. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-0981-9_3.

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Brohé, Myrana, and Patricia Tossings. "Relaxed Assumptions for Iteration Methods." In Lecture Notes in Economics and Mathematical Systems, 83–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57014-8_6.

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Milius, Stefan, Jiří Adámek, and Henning Urbat. "On Algebras with Effectful Iteration." In Coalgebraic Methods in Computer Science, 144–66. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00389-0_9.

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Borwein, J. M., and P. B. Borwein. "A remarkable cubic mean iteration." In Computational Methods and Function Theory, 27–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0087894.

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Conference papers on the topic "Iteration methods"

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Al-Mohssen, Husain A., Nicolas G. Hadjiconstantinou, and Ioannis G. Kevrekidis. "Acceleration Methods for Coarse-Grained Numerical Solution of the Boltzmann Equation." In ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2006. http://dx.doi.org/10.1115/icnmm2006-96119.

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We present a coarse-grained steady state solution framework for the Boltzmann kinetic equation based on a Newton-Broyden iteration. This approach is an extension of the equation-free framework proposed by Kevrekidis and coworkers, whose objective is the use of fine-scale simulation tools to directly extract coarse-grained, macroscopic information. Our current objective is the development of efficient simulation tools for modeling complex micro/nanoscale flows. The iterative method proposed and used here consists of a short Boltzmann transient evolution step and a Newton-Broyden contraction mapping step based on the Boltzmann solution; the latter step only solves for the macroscopic field of interest (e.g. flow velocity). The predicted macroscopic field is then used as an initial condition for the Boltzmann solver for the next iteration. We have validated this approach for isothermal, one-dimensional flows in the low Knudsen number regime. We find that the Newton-Broyden iteration converges in O(10) iterations, starting from arbitrary guess solutions and a Navier-Stokes based initial Jacobian. This results in computational savings compared to time-explicit integration to steady states when the time to steady state is longer than O(40) mean collision times.
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Spiridonov, Alexander O., and Evgenii M. Karchevskii. "Residual Inverse Iteration for the Lasing Eigenvalue Problem." In 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET). IEEE, 2018. http://dx.doi.org/10.1109/mmet.2018.8460224.

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Divo, Eduardo, Alain J. Kassab, Eric Mitteff, and Luis Quintana. "A Parallel Domain Decomposition Technique for Meshless Methods Applications to Large-Scale Heat Transfer Problems." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56004.

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Mesh reduction methods such as the boundary element methods, method of fundamental solutions or the so-called meshless methods all lead to fully populated matrices. This poses serious challenges for large-scale three-dimensional problems due to storage requirements and iterative solution of a large set of non-symmetric equations. Researchers have developed several approaches to address this issue including the class of fast-multipole techniques, use of wavelet transforms, and matrix decomposition. In this paper, we develop a domain-decomposition, or the artificial sub-sectioning technique, along with a region-by-region iteration algorithm particularly tailored for parallel computation to address the coefficient matrix issue. The meshless method we employ is based on expansions using radial basis functions (RBFs). An efficient physically-based procedure provides an effective initial guess of the temperatures along the sub-domain interfaces. The iteration process converges very efficiently, offers substantial savings in memory, and features superior computational efficiency. The meshless iterative domain decomposition technique is ideally suited for parallel computation. We discuss its implementation under MPI standards on a small Windows XP PC cluster. Numerical results reveal the domain decomposition meshless methods produce accurate temperature predictions while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.
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Arslan, Oktay, and Panagiotis Tsiotras. "Incremental sampling-based motion planners using policy iteration methods." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7799034.

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Sun, Wei, Xiao-Guang Fan, and Tong Wang. "Efficient Iteration methods for Constrained Multibody Dynamics & Symposia." In 2014 11th IEEE International Conference on Control & Automation (ICCA). IEEE, 2014. http://dx.doi.org/10.1109/icca.2014.6871028.

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Tiwari, Abhishek, Kaveh A. Tagavi, and J. M. McDonough. "Analytical Methods for Transport Equations in Similarity Form." In ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference collocated with the ASME 2007 InterPACK Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ht2007-32294.

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We present a novel approach for deriving analytical solutions to transport equations expressed in similarity variables. We apply a fixed-point iteration procedure to these transformed equations by formally solving for the highest derivative term and, from this (via requirements for convergence given by the contraction mapping principle), deduce a range of values for the outer limit of solution domain, for which the fixed-point iteration gives a converged solution.
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Urniezius, Renaldas, and Adom Giffin. "Iteration free vector orientation using maximum relative entropy with observational priors." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2012. http://dx.doi.org/10.1063/1.3703634.

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Lambers, James V. "Enhancement of Krylov Subspace Spectral Methods by Block Lanczos Iteration." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990930.

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Kosi, Krisztian. "Generalized Approximate Model for "Fixed Point Iteration"- Based Control Methods." In 2021 IEEE 25th International Conference on Intelligent Engineering Systems (INES). IEEE, 2021. http://dx.doi.org/10.1109/ines52918.2021.9512903.

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Thompson, Lonny L., and Prapot Kunthong. "Stabilized Time-Discontinuous Galerkin Methods With Applications to Structural Acoustics." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15753.

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The time-discontinuous Galerkin (TDG) method possesses high-order accuracy and desirable C-and L-stability for second-order hyperbolic systems including structural acoustics. C- and L-stability provide asymptotic annihilation of high frequency response due to spurious resolution of small scales. These non-physical responses are due to limitations in spatial discretization level for large-complex systems. In order to retain the high-order accuracy of the parent TDG method for high temporal approximation orders within an efficient multi-pass iterative solution algorithm which maintains stability, generalized gradients of residuals of the equations of motion expressed in state-space form are added to the TDG variational formulation. The resultant algorithm is shown to belong to a family of Pade approximations for the exponential solution to the spatially discrete hyperbolic equation system. The final form of the algorithm uses only a few iteration passes to reach the order of accuracy of the parent solution. Analysis of the multi-pass algorithm shows that the first iteration pass belongs to the family of (p+1)-stage stiff accurate Singly-Diagonal-Implicit-Runge-Kutta (SDIRK) method. The methods developed can be viewed as a generalization to the SDIRK method, retaining the desirable features of efficiency and stability, now extended to high-order accuracy. An example of a transient solution to the scalar wave equation demonstrates the efficiency and accuracy of the multi-pass algorithms over standard second-order accurate single-step/single-solve (SS/SS) methods.
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Reports on the topic "Iteration methods"

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Li, Zhilin, and Kazufumi Ito. Subspace Iteration and Immersed Interface Methods: Theory, Algorithm, and Applications. Fort Belvoir, VA: Defense Technical Information Center, August 2010. http://dx.doi.org/10.21236/ada532686.

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Dmitriy Y. Anistratov, Adrian Constantinescu, Loren Roberts, and William Wieselquist. Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids. Office of Scientific and Technical Information (OSTI), April 2007. http://dx.doi.org/10.2172/909188.

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Wemhoff, A., A. Burnham, B. de Supinski, J. Sexton, and J. Gunnels. Methods for Calibration of Prout-Tompkins Kinetics Parameters Using EZM Iteration and GLO. Office of Scientific and Technical Information (OSTI), November 2006. http://dx.doi.org/10.2172/898464.

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Tapia, Richard A., Yin Zhang, and Yinyu Ye. On the Convergence of the Iteration Sequence in Primal-Dual Interior-Point Methods. Fort Belvoir, VA: Defense Technical Information Center, August 1993. http://dx.doi.org/10.21236/ada452704.

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Миненко, П. А. Обратная нелинейная задача гравиметрии на основе аналогов фильтров Винера–Калмана. Нацiональна академiя наук України, 2008. http://dx.doi.org/10.31812/123456789/5214.

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An iterative method of solution of a nonlinear inverse problem of gravimetry on the basis of the joint application of several cards of the measured field and several vectors of entry conditions for depths up to blocks of rocks in one iteration is developed. Examples of the interpretation of the gravitational field measured in the Western Krivbass are given.
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Holliday, D., L. L. Jr DeRaad, and G. J. St-Cyr. Wedge scattering by the method of iteration. Office of Scientific and Technical Information (OSTI), July 1993. http://dx.doi.org/10.2172/10144586.

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Sezer, Sefa A., and Ibrahim Çanak. Tauberian Remainder Theorems for Iterations of Methods of Weighted Means. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2019. http://dx.doi.org/10.7546/crabs.2019.01.01.

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Cai, X.-C. Scalable nonlinear iterative methods for partial differential equations. Office of Scientific and Technical Information (OSTI), October 2000. http://dx.doi.org/10.2172/15013129.

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Foulser, David E. Highly Parallel Iterative Methods for Massively Parallel Multiprocessors. Fort Belvoir, VA: Defense Technical Information Center, February 1989. http://dx.doi.org/10.21236/ada206305.

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Shiau, Tzong H. Iterative Methods for Linear Complementary and Related Problems. Fort Belvoir, VA: Defense Technical Information Center, May 1989. http://dx.doi.org/10.21236/ada212848.

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