Relevant bibliographies by topics / Implicit iteration

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

Academic literature on the topic 'Implicit iteration'

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Published: 3 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Implicit iteration"

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Chugh, Renu, Preety Malik, and Vivek Kumar. "On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces." Journal of Function Spaces 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/905834.

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The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented.
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Joodi, Omar Mohammed Abbas, and Zena Hussein Maibed. "On analytical convergence of multi iterative procedure for finite family of generalized contractive." Journal of Interdisciplinary Mathematics 26, no. 7 (2023): 1635–46. http://dx.doi.org/10.47974/jim-1654.

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This paper introduces new iterations type three steps as multi_ implicit Noor iteration, multi_explicit Noor iteration and multi_Picard S-iteration, and defines a generalized quasi-like contractive mapping in convex metric space. Also, the convergence and stability of it are studied. On the other hand, the multi_ implicit Noor iteration is faster than the multi_explicit Noor iteration and multi_Picard S-iteration
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Wang, Cheng, and Zhi Ming Wang. "The Equivalence of Mann and Implicit Mann Iterations for Uniformly Pseudocontractive Mappings in Uniformly Smooth Banach Spaces." Applied Mechanics and Materials 50-51 (February 2011): 718–22. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.718.

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In this paper, suppose is an arbitrary uniformly smooth real Banach space, and is a nonempty closed convex subset of . Let be a generalized Lipschitzian and uniformly pseudocontractive self-map with . Suppose that , are defined by Mann iteration and implicit Mann iteration respectively, with the iterative parameter satisfying certain conditions. Then the above two iterations that converge strongly to fixed point of are equivalent.
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Rhoades, B. E., and Ştefan M. Şoltuz. "The convergence of an implicit mean value iteration." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–7. http://dx.doi.org/10.1155/ijmms/2006/68369.

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Sablin, M. "An iterative method for solving difference problems of gas dynamics in the mixed Euler-Lagrangian variables." Journal of Physics: Conference Series 2099, no. 1 (2021): 012013. http://dx.doi.org/10.1088/1742-6596/2099/1/012013.

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Abstract The method proposed is intended to solve implicit conservative operator difference schemes for a grid initial-boundary value problems on a simplex grid for a system of equations of gas dynamics in the mixed Euler-Lagrangian variables. To find a solution to such a scheme at a time step, it is represented as a single equation for a nonlinear function of two arguments from space – the direct product of the grid spaces of gas-dynamic quantities. To solve such an equation, a combination of the generalized Gauss-Seidel iterative method (external iterations) and an implicit two-layer iteration scheme (internal iterations at each external iteration) is used. The feature of the method is that, the equation, which is solved by internal iterations, is obtained from the equation of the difference scheme using symmetrization – such a non-degenerate linear transformation that the function in this equation has a self-adjoint positive Frechet derivative.
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YEE, H. C., and P. K. SWEBY. "GLOBAL ASYMPTOTIC BEHAVIOR OF ITERATIVE IMPLICIT SCHEMES." International Journal of Bifurcation and Chaos 04, no. 06 (1994): 1579–611. http://dx.doi.org/10.1142/s0218127494001210.

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The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2×2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.
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Yildirim, Isa, and Mujahid Abbas. "Convergence Rate of Implicit Iteration Process and a Data Dependence Result." European Journal of Pure and Applied Mathematics 11, no. 1 (2018): 189. http://dx.doi.org/10.29020/nybg.ejpam.v11i1.2911.

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The aim of this paper is to introduce an implicit S-iteration processand study its convergence in the framework of W-hyperbolic spaces. We showthat the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.
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Agwu, Imo Kalu, Umar Ishtiaq, Naeem Saleem, Donatus Ikechi Igbokwe, and Fahd Jarad. "Equivalence of novel IH-implicit fixed point algorithms for a general class of contractive maps." AIMS Mathematics 8, no. 1 (2022): 841–72. http://dx.doi.org/10.3934/math.2023041.

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<abstract><p>In this paper, a novel implicit IH-multistep fixed point algorithm and convergence result for a general class of contractive maps is introduced without any imposition of the "sum conditions" on the countably finite family of the iteration parameters. Furthermore, it is shown that the convergence of the proposed iteration scheme is equivalent to some other implicit IH-type iterative schemes (e.g., implicit IH-Noor, implicit IH-Ishikawa and implicit IH-Mann) for the same class of maps. Also, some numerical examples are given to illustrate that the equivalence is true. Our results complement, improve and unify several equivalent results recently announced in literature.</p></abstract>
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Balicki, Linus. "Low-Rank Alternating Direction Implicit Iteration in pyMOR." GAMM Archive for Students 2, no. 1 (2020): 1–13. http://dx.doi.org/10.14464/gammas.v2i1.420.

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The low-rank alternating direction implicit (LR-ADI) iteration is an effective method for solving large-scale Lyapunov equations. In the software library pyMOR, solutions to Lyapunov equations play an important role when reducing a model using the balanced truncation method. In this article we introduce the LR-ADI iteration as well as pyMOR, while focusing on its features which are relevant for integrating the iteration into the library. We compare the run time of the iteration's pure pyMOR implementation with those achieved by external libraries available within the pyMOR framework.
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Li, Teng-fei, and Heng-you Lan. "On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications." Journal of Function Spaces 2019 (March 3, 2019): 1–13. http://dx.doi.org/10.1155/2019/4042965.

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In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. Further, some numerical examples and applications to optimal control problems with elliptic boundary value constraints are considered via the new Picard-Mann iterative approximations, which shows that the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes.
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Dissertations / Theses on the topic "Implicit iteration"

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Toulis, Panagiotis. "Implicit methods for iterative estimation with large data sets." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493434.

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The ideal estimation method needs to fulfill three requirements: (i) efficient computation, (ii) statistical efficiency, and (iii) numerical stability. The classical stochastic approximation of (Robbins, 1951) is an iterative estimation method, where the current iterate (parameter estimate) is updated according to some discrepancy between what is observed and what is expected assuming the current iterate has the true parameter value. Classical stochastic approximation undoubtedly meets the computation requirement, which explains its widespread popularity, for example, in modern applications of machine learning with large data sets, but cannot effectively combine it with efficiency and stability. Surprisingly, the stability issue can be improved substantially, if the aforementioned discrepancy is computed not using the current iterate, but using the conditional expectation of the next iterate given the current one. The computational overhead of the resulting implicit update is minimal for many statistical models, whereas statistical efficiency can be achieved through simple averaging of the iterates, as in classical stochastic approximation (Ruppert, 1988). Thus, implicit stochastic approximation is fast and principled, fulfills requirements (i-iii) for a number of popular statistical models including generalized linear models, M-estimation, and proportional hazards, and it is poised to become the workhorse of estimation with large data sets in statistical practice.<br>Statistics
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Cai, Shang-Gui. "Computational fluid-structure interaction with the moving immersed boundary method." Thesis, Compiègne, 2016. http://www.theses.fr/2016COMP2276/document.

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Dans cette thèse, une nouvelle méthode de frontières immergées a été développée pour la simulation d'interaction fluide-structure, appelée la méthode de frontières immergées mobiles (en langage anglo-saxon: MIBM). L'objectif principal de cette nouvelle méthode est de déplacer arbitrairement les solides à géométrie complexe dans un fluide visqueux incompressible, sans remailler le domaine fluide. Cette nouvelle méthode a l'avantage d'imposer la condition de non-glissement à l'interface d'une manière exacte via une force sans introduire des constantes artificielles modélisant la structure rigide. Cet avantage conduit également à la satisfaction de la condition CFL avec un pas de temps plus grand. Pour un calcul précis de la force induite par les frontières mobiles, un système linéaire a été introduit et résolu par la méthode de gradient conjugué. La méthode proposée peut être intégrée facilement dans des solveurs résolvant les équations de Navier-Stokes. Dans ce travail la MIBM a été mise en œuvre en couplage avec un solveur fluide utilisant une méthode de projection adaptée pour obtenir des solutions d'ordre deux en temps et en espace. Le champ de pression a été obtenu par l'équation de Poisson qui a été résolue à l'aide de la méthode du gradient conjugué préconditionné par la méthode multi-grille. La combinaison de ces deux méthodes a permis un gain de temps considérable par rapport aux méthodes classiques de la résolution des systèmes linéaires. De plus le code de calcul développé a été parallélisé sur l'unité graphique GPU équipée de la bibliothèque CUDA pour aboutir à des hautes performances de calcul. Enfin, comme application de nos travaux sur la MIBM, nous avons étudié le couplage "fort" d'interaction fluide-structure (IFS). Pour ce type de couplage, un schéma implicite partitionné a été adopté dans lequel les conditions à l'interface sont satisfaites via un schéma de type "point fixe". Pour réduire le temps de calcul inhérent à cette application, un nouveau schéma de couplage a été proposé pour éviter la résolution de l'équation de Poisson durant les itérations du "point fixe". Cette nouvelle façon de résoudre les problèmes IFS a montré des performances prometteuses pour des systèmes en IFS complexe<br>In this thesis a novel non-body conforming mesh formulation is developed, called the moving immersed boundary method (MIBM), for the numerical simulation of fluid-structure interaction (FSI). The primary goal is to enable solids of complex shape to move arbitrarily in an incompressible viscous fluid, without fitting the solid boundary motion with dynamic meshes. This novel method enforces the no-slip boundary condition exactly at the fluid-solid interface with a boundary force, without introducing any artificial constants to the rigid body formulation. As a result, large time step can be used in current method. To determine the boundary force more efficiently in case of moving boundaries, an additional moving force equation is derived and the resulting system is solved by the conjugate gradient method. The proposed method is highly portable and can be integrated into any fluid solver as a plug-in. In the present thesis, the MIBM is implemented in the fluid solver based on the projection method. In order to obtain results of high accuracy, the rotational incremental pressure correction projection method is adopted, which is free of numerical boundary layer and is second order accurate. To accelerate the calculation of the pressure Poisson equation, the multi-grid method is employed as a preconditioner together with the conjugate gradient method as a solver. The code is further parallelized on the graphics processing unit (GPU) with the CUDA library to enjoy high performance computing. At last, the proposed MIBM is applied to the study of two-way FSI problem. For stability and modularity reasons, a partitioned implicit scheme is selected for this strongly coupled problem. The interface matching of fluid and solid variables is realized through a fixed point iteration. To reduce the computational cost, a novel efficient coupling scheme is proposed by removing the time-consuming pressure Poisson equation from this fixed point interaction. The proposed method has shown a promising performance in modeling complex FSI system
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Ahmed, Nisar. "Implicit restart schemes for Krylov subspace model reduction methods." Thesis, Imperial College London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340535.

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Swarup, A. Sri Sakti. "Implicit Least Squares Kinetic Upwind Method (LSKUM) And Implicit LSKUM Based On Entropy Variables (q-LSKUM)." Thesis, Indian Institute of Science, 2000. https://etd.iisc.ac.in/handle/2005/239.

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With increasing demand for computational solutions of fluid dynamical problems, researchers around the world are working on the development of highly robust numerical schemes capable of solving flow problems around complex geometries arising in Aerospace engineering. Also considerable time and effort are devoted to development of convergence acceleration devices, for reducing the computational time required for such numerical solutions. Reduction in run times is very vital for production codes which are used many times in design cycle. In this present work, we consider a numerical scheme called LSKUM capable of operating on any arbitrary distribution of points. LSKUM is being used in CFD center (IIsc) and DRDL (Hyderabad) to compute flows around practical geometries and presently these LSKUM based codes are explicit- It has been observed already by the earlier researchers that the explicit schemes for these methods are robust. Therefore, it is absolutely essential to consider the possibility of accelerating explicit LSKUM by making it LSKUM-Implicit. The present thesis focuses on such a study. We start with two kinetic schemes namely Least Squares Kinetic Upwind Method (LSKUM) and LSKUM based on entropy variables (q-LSKUM). We have developed the following two implicit schemes using LSKUM and q-LSKUM. They are (i)Non-Linear Iterative Implicit Scheme called LSKUM-NII. (ii)Linearized Beam and Warming implicit Scheme, called LSKUM-BW. For the purpose of demonstration of efficiency of the newly developed above implicit schemes, we have considered flow past NACA0012 airfoil as a test example. In this regard we have tested these implicit schemes for flow regimes mentioned below •Subsonic Case: M∞ = 0.63, a.o.a = 2.0° •Transonic Case: M∞ = 0.85, a.o.a = 1.0° The speedup of the above two implicit schemes has been studied in this thesis by operating them on different grid sizes given below •Coarse Grid: 4074 points •Medium Grid: 8088 points •Fine Grid: 16594 points The results obtained by running these implicit schemes are found to be very much encouraging. It has been observed that these newly developed implicit schemes give as much as 2.8 times speedup compared to their corresponding explicit versions. Further improvement is possible by combining LKSUM-Implicit with modern iterative methods of solving resultant algebraic equations. The present work is a first step towards this objective.
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Swarup, A. Sri Sakti. "Implicit Least Squares Kinetic Upwind Method (LSKUM) And Implicit LSKUM Based On Entropy Variables (q-LSKUM)." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/239.

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With increasing demand for computational solutions of fluid dynamical problems, researchers around the world are working on the development of highly robust numerical schemes capable of solving flow problems around complex geometries arising in Aerospace engineering. Also considerable time and effort are devoted to development of convergence acceleration devices, for reducing the computational time required for such numerical solutions. Reduction in run times is very vital for production codes which are used many times in design cycle. In this present work, we consider a numerical scheme called LSKUM capable of operating on any arbitrary distribution of points. LSKUM is being used in CFD center (IIsc) and DRDL (Hyderabad) to compute flows around practical geometries and presently these LSKUM based codes are explicit- It has been observed already by the earlier researchers that the explicit schemes for these methods are robust. Therefore, it is absolutely essential to consider the possibility of accelerating explicit LSKUM by making it LSKUM-Implicit. The present thesis focuses on such a study. We start with two kinetic schemes namely Least Squares Kinetic Upwind Method (LSKUM) and LSKUM based on entropy variables (q-LSKUM). We have developed the following two implicit schemes using LSKUM and q-LSKUM. They are (i)Non-Linear Iterative Implicit Scheme called LSKUM-NII. (ii)Linearized Beam and Warming implicit Scheme, called LSKUM-BW. For the purpose of demonstration of efficiency of the newly developed above implicit schemes, we have considered flow past NACA0012 airfoil as a test example. In this regard we have tested these implicit schemes for flow regimes mentioned below •Subsonic Case: M∞ = 0.63, a.o.a = 2.0° •Transonic Case: M∞ = 0.85, a.o.a = 1.0° The speedup of the above two implicit schemes has been studied in this thesis by operating them on different grid sizes given below •Coarse Grid: 4074 points •Medium Grid: 8088 points •Fine Grid: 16594 points The results obtained by running these implicit schemes are found to be very much encouraging. It has been observed that these newly developed implicit schemes give as much as 2.8 times speedup compared to their corresponding explicit versions. Further improvement is possible by combining LKSUM-Implicit with modern iterative methods of solving resultant algebraic equations. The present work is a first step towards this objective.
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Le, Chuiton Frédéric. "Une méthode implicite non-factorisée décentrée hybride pour la simulation numérique d'écoulements autour de géométries complexes." Ecully, Ecole centrale de Lyon, 1999. http://bibli.ec-lyon.fr/exl-doc/TH_T1781_flechuiton.pdf.

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Ce mémoire de thèse est consacré à l'étude d'un schéma numérique permettant, à terme, d'effectuer des calculs Navier-Stokes précis à l'aide d'une intégration Euler implicite non-factorisée. La discrétisation en espace est celle d'un schéma décentré hybride (HUS), d'après les travaux de Coquel &amp; Liou, qui conjugue le schéma de Perthame (FVS), fondé sur une interprétation cinétique des équations d'Euler, et le schéma de Osher (FDS). Le schéma ainsi bati préserve la robustesse des FVS, au travers des ondes non-linéaires, et la précision des FDS, pour la capture des ondes linéaires. L'opérateur implicite est construit par linéarisation du FVS à l'ordre un en espace et par linéarisation des conditions-limites aussi bien aux frontières physiques qu'aux frontières de raccord multi-domaines. Le système linéaire qui en résulte est inversé de manière approchée à l'aide d'un algorithme itératif de Krylov, ici Bi-CGStab dû à Van der Vorst, que l'on préconditionne par un autre algorithme itératif SSOR. La validation de l'opérateur spatial est effectuée sur des cas de tube à choc et sur un profil d'aile par comparaison avec le schéma de Jameson. Ensuite, l'intégration temporelle implicite est évaluée à l'aide de cas bidimensionnels, un canal avec bosse et le même profil d'aile, et à l'aide de cas tridimensionnels, une nacelle isolée et une configuration comprenant un tronçon d'aile, un mât et une nacelle perméable. Ces études mettent en évidence, d'une part, la nette amélioration de la représentation des sillages et la réduction des pertes de pression totale obtenue à l'aide du schéma hybride par rapport à un FVS seul et, d'autre part, le bien fondé de l'implicitation des conditions-limites, de l'augmentation forcée du CFL, d'une résolution seulement approchée du système linéaire et du préconditionnement itératif<br>This thesis dissertation aims at studying a numerical scheme that allows accurate Navier-Stokes computations using an Euler implicit non-factorised integration. The spatial operator has been constructed by the combination of the scheme of Perthame (FVS), based on a kinetic interpretation of the Euler equations, and of the scheme of Osher (FDS). This results in one member of the hybrid upwind scheme family (HUS) introduced by Coquel &amp; Liou, which retains the FVS robustness through non-linear waves and the FDS accuracy in capturing linear waves. The implicit operator is provided by the exact linearization of the FVS part, at first order in space, and by incorporating the boundary conditions, inter-block matching ones as well as physical ones. The subsequent linear system is approximately inverted by means of a Krylov algorithm, Bi-CGStab from Van der Vorst, and is preconditioned by an SSOR iterative method. The spatial discretization has been validated on shock tube problems and on an aerofoil profile by comparison with the scheme of Jameson. Then, the implicit integration has been assessed on bi-dimensional cases, a channel with a bump and the same aerofoil profile, and on three-dimensional cases, an isolated nacelle and a full configuration made of a truncated wing, a pylon and a nacelle. Numerical tests have demonstrated, on the one hand, a serious improvement in capturing wakes and in reducing total pressure losses, due to the hybrid scheme over a simple FVS scheme and, on the other hand, the relevance of implicit boundary conditions, the constant increase of the CFL number, a mere approximate inversion of the linear system and the efficiency of the iterative preconditioner
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Bílý, Vojtěch. "Detekce a sledování objektů pomocí význačných bodů." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236598.

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This paper deals with object detection and tracking using iterest points. Existing approaches are described here. Inovated method based on Generalized Hough transform and iterative Hough-space searching is  proposed in this paper. Generality of proposed detector is shown in various types of objects. Object tracking is designed as frame by frame detection.
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Shepherd, David. "Numerical methods for dynamic micromagnetics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/numerical-methods-for-dynamic-micromagnetics(e8c5549b-7cf7-44af-8191-5244a491d690).html.

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Micromagnetics is a continuum mechanics theory of magnetic materials widely used in industry and academia. In this thesis we describe a complete numerical method, with a number of novel components, for the computational solution of dynamic micromagnetic problems by solving the Landau-Lifshitz-Gilbert (LLG) equation. In particular we focus on the use of the implicit midpoint rule (IMR), a time integration scheme which conserves several important properties of the LLG equation. We use the finite element method for spatial discretisation, and use nodal quadrature schemes to retain the conservation properties of IMR despite the weak-form approach. We introduce a novel, generally-applicable adaptive time step selection algorithm for the IMR. The resulting scheme selects error-appropriate time steps for a variety of problems, including the semi-discretised LLG equation. We also show that it retains the conservation properties of the fixed step IMR for the LLG equation. We demonstrate how hybrid FEM/BEM magnetostatic calculations can be coupled to the LLG equation in a monolithic manner. This allows the coupled solver to maintain all properties of the standard time integration scheme, in particular stability properties and the energy conservation property of IMR. We also develop a preconditioned Krylov solver for the coupled system which can efficiently solve the monolithic system provided that an effective preconditioner for the LLG sub-problem is available. Finally we investigate the effect of the spatial discretisation on the comparative effectiveness of implicit and explicit time integration schemes (i.e. the stiffness). We find that explicit methods are more efficient for simple problems, but for the fine spatial discretisations required in a number of more complex cases implicit schemes become orders of magnitude more efficient.
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Lehoucq, Richard Bruno. "Analysis and implementation of an implicitly restarted Arnoldi iteration." Thesis, 1995. http://hdl.handle.net/1911/16844.

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The Arnoldi algorithm, or iteration, is a computationally attractive technique for computing a few eigenvalues and associated invariant subspace of large, often sparse, matrices. The method is a generalization of the Lanczos process and reduces to that when the underlying matrix is symmetric. This thesis presents an analysis of Sorensen's Implicitly Re-started Arnoldi iteration, (scIRA-iteration), by exploiting its relationship with the scQR algorithm. The goal of this thesis is to present numerical techniques that attempt to make the scIRA-iteration as robust as the implicitly shifted scQR algorithm. The benefit is that the Arnoldi iteration only requires the computation of matrix vector products w = Av at each step. It does to rely on the dense matrix similarity transformations required by the EISPACK and LAPACK software packages. Five topics form the contribution of this dissertation. The first topic analyzes re-starting the Arnoldi iteration in an implicit or explicit manner. The second topic is the numerical stability of an scIRA-iteration. The forward instability of the scQR algorithm and the various schemes used to re-order the Schur form of a matrix are fundamental to this analysis. A sensitivity analysis of the Hessenberg decomposition is presented. The practical issues associated with maintaining numerical orthogonality among the Arnoldi/Lanczos basis vectors is the third topic. The fourth topic is deflation techniques for an scIRA-iteration. The deflation strategies introduced make it possible to compute multiple or clustered eigenvalues with a single vector re-start method. The block Arnoldi/Lanczos methods commonly used are not required. The final topic is the convergence typical of an scIRA-iteration. Both formal theory and heuristics are provided for making choices that will lead to improved convergence of an scIRA-iteration.
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Pollul, Bernhard [Verfasser]. "Iterative solvers in implicit time integration for compressible flows / vorgelegt von Bernhard Pollul." 2008. http://d-nb.info/991566092/34.

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Books on the topic "Implicit iteration"

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Saylor, Paul E. Linear iterative solvers for implicit ode methods. National Aeronautics and Space Administration, Langley Research Center, 1990.

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-S, Liu N., Kim Hyun Dae, and United States. National Aeronautics and Space Administration., eds. An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations. National Aeronautics and Space Administration, 1991.

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An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations. National Aeronautics and Space Administration, 1991.

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Lattman, Eaton E., Thomas D. Grant, and Edward H. Snell. Pushing the Envelope. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199670871.003.0014.

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Direct electron density determination from SAXS data opens up new opportunities. The ability to model density at high resolution and the implicit direct estimation of solvent terms such as the hydration shell may enable high-resolution wide angle scattering data to be used to calculate density when combined with additional structural information. Other diffraction methods that do not measure three-dimensional intensities, such as fiber diffraction, may also be able to take advantage of iterative structure factor retrieval. While the ability to reconstruct electron density ab initio is a major breakthrough in the field of solution scattering, the potential of the technique has yet to be fully uncovered. Additional structural information from techniques such as crystallography, NMR, and electron microscopy and density modification procedures can now be integrated to perform advanced modeling of the electron density function at high resolution, pushing the boundaries of solution scattering further than ever before.
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Book chapters on the topic "Implicit iteration"

1

Eidelman, Yuli, Israel Gohberg, and Iulian Haimovici. "The Implicit QR Iteration Method for Eigenvalues of Upper Hessenberg Matrices." In Separable Type Representations of Matrices and Fast Algorithms. Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0612-1_11.

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Wu, Zi-Niu, and Hui Zou. "Parallel Computation of Compressible Flows for Implicit Schemes Without Sub-iteration and Modification of the Implicit Solver." In Computational Fluid Dynamics for the 21st Century. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44959-1_13.

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Li-mei, Liu, Li Xiu-Yun, and Zuo Ya-Li. "Convergence of an Implicit Iteration Process with Errors for ϕ Strictly Pseudocontractive Mappings." In Lecture Notes in Electrical Engineering. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40630-0_52.

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Elistratov, Andrei A., Dmitry V. Savin, and Olga B. Isaeva. "Complex Dynamics of the Implicit Maps Derived from Iteration of Newton and Euler Methods." In Communications in Computer and Information Science. Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-24145-1_3.

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Qin, Junwei, and Yunzhao Li. "Three-Dimensional Pin-by-Pin Transient Analysis for PWR-Core." In Springer Proceedings in Physics. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-1023-6_67.

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AbstractTo ensure the safety of PWR-core operation, three-dimensional whole-core transient analysis needs to be carried out for the sake of the pin-power distribution. For this purpose, this paper presents “Bamboo-Transient 2.0”, a three-dimensional pin-by-pin transient analysis program. The program adopts a fully-implicit backward method with finite difference for time variable discretization, a method of exponential function expansion nodal (EFEN) SP3 for the neutron transport calculation, and a multi-channel model for the thermal feedback calculation. In addition, Picard iteration is used to couple the neutronics with thermal-feedback, which is intended to guarantee the convergence of coupling iteration at each time step. Moreover, the program can perform parallel computing based on Message Passing Interface (MPI) for the whole-core pin-by-pin transient analysis. This developed program has been applied to two commercial PWRs, viz. AP1000 and CNP1000. Numerical results of this application demonstrate that Bamboo-Transient 2.0 can yield much more refined results than the traditional legacy coarse-mesh neutron-diffusion programs based on assembly homogenization. Its pin-wise distributions of state parameters are reliable and thus can satisfactorily meet the requirements and purpose of safety analysis.
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Xiaomin, Chen, Xie Xuping, and Duan Qibin. "Approximation of Implicit Iteration Process for Common Fixed Point of Composite General Asymptotically Nonexpansive Mappings." In Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31698-2_98.

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Varga, Richard S. "Alternating-Direction Implicit Iterative Methods." In Matrix Iterative Analysis. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05156-2_7.

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Koepf, Wolfram. "Implizite Funktionen und Iteration." In Höhere Analysis mit DERIVE. Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-83118-7_3.

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Sima, Vasile, and Pascal Gahinet. "Alternating Implicit and Semi-implicit Iterations in the Periodic QZ Algorithm." In Informatics in Control, Automation and Robotics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-92442-3_4.

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Sawitzki, Daniel. "Implicit Flow Maximization by Iterative Squaring." In SOFSEM 2004: Theory and Practice of Computer Science. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24618-3_26.

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Conference papers on the topic "Implicit iteration"

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Zhang, Yuxuan, Dingxi Wang, Sen Zhang, and Yuze Zhu. "Numerical Stability Analysis of Implicit Solution Methods for Harmonic Balance Equations." In ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/gt2024-125758.

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Abstract This paper presents an investigation into the numerical stability of various implicit solution methods for an efficient solution of harmonic balance equations for turbomachinery unsteady flows. Those implicit solution methods were proposed to enhance stability and accelerate the convergence of harmonic balance solutions by implicitly integrating the time spectral source term of a harmonic balance equation. They include the block Jacobi method (BJ), the Jacobi iteration method (JI), and their variants, i.e. the modified block Jacobi method (MBJ) and the modified Jacobi iteration method (MJI). These implicit treatments are typically combined with the lower upper symmetric Gauss-Seidel method (LU-SGS) as a preconditioner of a Runge-Kutta scheme. In this study, the von Neumann analysis is applied to evaluate the stability and damping properties of all these methods. The findings reveal that the LU-SGS/BJ and LU-SGS/MJI schemes can allow larger Courant numbers, in the order of hundreds, leading to a significant convergence speedup, while the LU-SGS/MBJ and LU-SGS/JI schemes fail to stabilize the solution, resulting in a Courant number below 10 as the grid-reduced frequency increases. The stabilization effect of the number of Jacobi iterations is also investigated. It is found that the minimum allowable relaxation factor does not change monotonically with the number of Jacobi iterations. Typically 2–4 Jacobi iterations are suggested for the stability and computational efficiency consideration, while any value larger than 4 is not recommended. The stability analysis results are numerically verified by solving the harmonic balance equation system for two cases. One is the inviscid flow over a two-dimensional bump with a pressure disturbance at the outlet. The other is the turbulent flow in a three-dimensional transonic compressor stage.
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Rajaomazava, Tolotra Emerry, Mustapha Benaouicha, and Jacques-Andre´ Astolfi. "A Comparison Study of Coupling Algorithms for Fluid-Structure Interaction Problems." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57573.

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The influence of numerical schemes for solving coupled problem in fluid-structure interaction is addressed. A non-linear Burgers equation in a bounded domain with moving interface is solved by finite element method (FEM). The implicit and explicit coupling algorithms are studied with interface equation solved at outside then inside of Newton iterative procedure (referred to as implicit-outer, implicit-inner, explicit and semi-implicit schemes respectively). Iteration numbers and computing time are compared for each algorithm. The interface position and energy conservation condition at the interface are discussed.
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Hu, Yujing, Yingfeng Chen, Changjie Fan, and Jianye Hao. "Explicitly Coordinated Policy Iteration." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/51.

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Coordination on an optimal policy between independent learners in fully cooperative stochastic games is difficult due to problems such as relative overgeneralization and miscoordination. Most state-of-the-art algorithms apply fusion heuristics on agents' optimistic and average rewards, by which coordination between agents can be achieved implicitly. However, such implicit coordination faces practical issues such as tedious parameter-tuning in real world applications. The lack of an explicit coordination mechanism may also lead to a low likelihood of coordination in problems with multiple optimal policies. Based on the necessary conditions of an optimal policy, we propose the explicitly coordinated policy iteration (EXCEL) algorithm which always forces agents to coordinate by comparing the agents' separated optimistic and average value functions. We also propose three solutions for deep reinforcement learning extensions of EXCEL. Extensive experiments in matrix games (from 2-agent 2-action games to 5-agent 20-action games) and stochastic games (from 2-agent games to 5-agent games) show that EXCEL has better performance than the state-of-the-art algorithms (such as faster convergence and better coordination).
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Liu, Chao, and Chun-song Gao. "Joint Iteration Method of unloaded Cable Shape and Pre-displacement of Main Cable Saddle for Long-span Suspension Bridges." In IABSE Symposium, Istanbul 2023: Long Span Bridges. International Association for Bridge and Structural Engineering (IABSE), 2023. http://dx.doi.org/10.2749/istanbul.2023.0904.

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&lt;p&gt;In this paper, a new method for calculating the unloaded cable shape and main cable saddle pre-displacement in the construction of long-span suspension bridges is proposed, which is called the joint iterative method (JIM). In this method, the first iteration does not require presupposing the saddle pre-displacement, and the results of the unloaded cable shape obtained in each subsequent iteration cycle will be mined to guide the saddle pre-displacement correction in the next iteration. This method uses simplified cable models and convergence conditions different from classical methods. In the simplified model of main cable mechanics, equal horizontal component of suspension bridge on both sides of main tower is taken as implicit condition, and equal unstressed cable length of each span of main cable is taken as convergence condition in iteration. Using this method, the pre-displacement of the main saddle and the unloaded cable shape of the Yingwuzhou Yangtze River Bridge is calculated by MATLAB program and compared with its designed value. The results show that this method requires few iterations and has high speed and accuracy.&lt;/p&gt;
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Maddulapalli, K., S. Azarm, and A. Boyars. "Interactive Product Design Selection With an Implicit Value Function." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dac-34080.

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We present an automated method to aid a Decision Maker (DM) in selecting the ‘most preferred’ from a set of design alternatives. The method assumes that the DM’s preferences reflect an implicit value function that is quasi-concave. The method is iterative, using three approaches in sequence to eliminate lower-value alternatives at each trial design. The method is interactive, with the DM stating preferences in the form of attribute tradeoffs at each trial design. We present an approach for finding a new trial design at each iteration. We provide an example, the design selection for a cordless electric drill, to demonstrate the method.
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Shim, P. Y., and S. Mannoochehri. "A Hybrid Shape Optimization Method Based on Implicit Differentiation and Node Removal Techniques." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0434.

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Abstract This paper presents a hybrid shape optimal design methodology using an implicit differentiation approach for sensitivity analysis and a node removal technique for shape alteration. The approach presented attempts to overcome the weaknesses inherent in each individual technique. The basic idea is to combine the sensitivity analysis, which forms the analytical basis for the algorithm, and a node removal technique, which grossly modifies the shape without the need for a remeshing after each iteration. The sensitivity analysis is based on the finite element equilibrium equation and the implicit differentiation technique. It examines the effect positional changes of the boundary nodes have on the stress values. Using the sensitivity results, a sequential linear programming algorithm is utilized to determine optimum positions of the boundary nodes. These optimization results are provided as inputs to an algorithm that decides which boundary nodes should be removed. By removing boundary nodes, the boundary elements change to either a triangular or a non-existent type. This shape modification procedure starts from the boundary elements and moves toward the internal elements. Only two iterations of finite element analysis are required to modify one boundary layer. To maintain the structural integrity and the connectivity of the elements in the model, a connectivity check is performed after each iteration. Three design examples are given to illustrate the accuracy and the steps involved in the proposed optimal design methodology.
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Yi, Sung-Jae, and Moon-Sun Chung. "An Advanced Semi-Implicit Method for Two-Phase Flow Calculation." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22009.

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Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the present authors’ reference: Numerical Heat Transfer —Part B, vol. 40, pp. 83–97. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. Owing to this modified numerical scheme with surface tension effect, the advanced semi-implicit method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity.
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Shen, Yiqing, Baoyuan Wang, and Gecheng Zha. "Comparison Study of Implicit Gauss-Seidel Line Iteration Method for Transonic Flows." In 18th AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-4332.

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Mosqueda, Gilberto, and Mehdi Ahmadizadeh. "Implicit numerical integration in hybrid simulation with iteration strategy for experimental substructures." In 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5160412.

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Geng, Zhang. "An Optimization Approach to the Shift Selection Problem in Alternating Direction Implicit Iteration." In 2010 Second International Conference on Computer Modeling and Simulation (ICCMS). IEEE, 2010. http://dx.doi.org/10.1109/iccms.2010.216.

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Reports on the topic "Implicit iteration"

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Lehoucq, R. B., and Danny C. Sorensen. Deflation Techniques for an Implicitly Re-started Arnoldi Iteration. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada447560.

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Alan B. Williams, Benjamin A. Allan, Kyran D. Mish, and Robert L. Clay. ISIS++Reference Guide (Iterative Scalable Implicit Solver in C++) Version 1.1. Office of Scientific and Technical Information (OSTI), 1999. http://dx.doi.org/10.2172/8238.

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de Kemp, E. A., H. A. J. Russell, B. Brodaric, et al. Initiating transformative geoscience practice at the Geological Survey of Canada: Canada in 3D. Natural Resources Canada/CMSS/Information Management, 2022. http://dx.doi.org/10.4095/331097.

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Application of 3D technologies to the wide range of Geosciences knowledge domains is well underway. These have been operationalized in workflows of the hydrocarbon sector for a half-century, and now in mining for over two decades. In Geosciences, algorithms, structured workflows and data integration strategies can support compelling Earth models, however challenges remain to meet the standards of geological plausibility required for most geoscientific studies. There is also missing links in the institutional information infrastructure supporting operational multi-scale 3D data and model development. Canada in 3D (C3D) is a vision and road map for transforming the Geological Survey of Canada's (GSC) work practice by leveraging emerging 3D technologies. Primarily the transformation from 2D geological mapping, to a well-structured 3D modelling practice that is both data-driven and knowledge-driven. It is tempting to imagine that advanced 3D computational methods, coupled with Artificial Intelligence and Big Data tools will automate the bulk of this process. To effectively apply these methods there is a need, however, for data to be in a well-organized, classified, georeferenced (3D) format embedded with key information, such as spatial-temporal relations, and earth process knowledge. Another key challenge for C3D is the relative infancy of 3D geoscience technologies for geological inference and 3D modelling using sparse and heterogeneous regional geoscience information, while preserving the insights and expertise of geoscientists maintaining scientific integrity of digital products. In most geological surveys, there remains considerable educational and operational challenges to achieve this balance of digital automation and expert knowledge. Emerging from the last two decades of research are more efficient workflows, transitioning from cumbersome, explicit (manual) to reproducible implicit semi-automated methods. They are characterized by integrated and iterative, forward and reverse geophysical modelling, coupled with stratigraphic and structural approaches. The full impact of research and development with these 3D tools, geophysical-geological integration and simulation approaches is perhaps unpredictable, but the expectation is that they will produce predictive, instructive models of Canada's geology that will be used to educate, prioritize and influence sustainable policy for stewarding our natural resources. On the horizon are 3D geological modelling methods spanning the gulf between local and frontier or green-fields, as well as deep crustal characterization. These are key components of mineral systems understanding, integrated and coupled hydrological modelling and energy transition applications, e.g. carbon sequestration, in-situ hydrogen mining, and geothermal exploration. Presented are some case study examples at a range of scales from our efforts in C3D.
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de Kemp, E. A., H. A. J. Russell, B. Brodaric, et al. Initiating transformative geoscience practice at the Geological Survey of Canada: Canada in 3D. Natural Resources Canada/CMSS/Information Management, 2023. http://dx.doi.org/10.4095/331871.

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Application of 3D technologies to the wide range of Geosciences knowledge domains is well underway. These have been operationalized in workflows of the hydrocarbon sector for a half-century, and now in mining for over two decades. In Geosciences, algorithms, structured workflows and data integration strategies can support compelling Earth models, however challenges remain to meet the standards of geological plausibility required for most geoscientific studies. There is also missing links in the institutional information infrastructure supporting operational multi-scale 3D data and model development. Canada in 3D (C3D) is a vision and road map for transforming the Geological Survey of Canada's (GSC) work practice by leveraging emerging 3D technologies. Primarily the transformation from 2D geological mapping, to a well-structured 3D modelling practice that is both data-driven and knowledge-driven. It is tempting to imagine that advanced 3D computational methods, coupled with Artificial Intelligence and Big Data tools will automate the bulk of this process. To effectively apply these methods there is a need, however, for data to be in a well-organized, classified, georeferenced (3D) format embedded with key information, such as spatial-temporal relations, and earth process knowledge. Another key challenge for C3D is the relative infancy of 3D geoscience technologies for geological inference and 3D modelling using sparse and heterogeneous regional geoscience information, while preserving the insights and expertise of geoscientists maintaining scientific integrity of digital products. In most geological surveys, there remains considerable educational and operational challenges to achieve this balance of digital automation and expert knowledge. Emerging from the last two decades of research are more efficient workflows, transitioning from cumbersome, explicit (manual) to reproducible implicit semi-automated methods. They are characterized by integrated and iterative, forward and reverse geophysical modelling, coupled with stratigraphic and structural approaches. The full impact of research and development with these 3D tools, geophysical-geological integration and simulation approaches is perhaps unpredictable, but the expectation is that they will produce predictive, instructive models of Canada's geology that will be used to educate, prioritize and influence sustainable policy for stewarding our natural resources. On the horizon are 3D geological modelling methods spanning the gulf between local and frontier or green-fields, as well as deep crustal characterization. These are key components of mineral systems understanding, integrated and coupled hydrological modelling and energy transition applications, e.g. carbon sequestration, in-situ hydrogen mining, and geothermal exploration. Presented are some case study examples at a range of scales from our efforts in C3D.
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