Hilbert Space Splittings And Iterative Methods

DOWNLOAD

Download Hilbert Space Splittings And Iterative Methods PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Hilbert Space Splittings And Iterative Methods book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Hilbert Space Splittings And Iterative Methods

DOWNLOAD
Author : Michael Griebel
language : en
Publisher: Springer Nature
Release Date : 2024-11-06

Hilbert Space Splittings And Iterative Methods written by Michael Griebel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.

This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxiliary variational problems on a set of (smaller, finite-dimensional) Hilbert spaces $V_i$ in a certain order, combining them, and using the combined approximations in an iterative procedure. The spaces $V_i$ form a so-called space splitting for V, they need not necessarily be subspaces of V, and their number can be finite or infinite. The convergence behavior of Schwarz methods is influenced by certain properties of the space splittings they are based on. These properties are identified, and a detailed treatment of traditional deterministic and more recent greedy and stochastic orderings in the subproblem solution process is given, together with an investigation of accelerated methods. To illustrate the abstract theory, the numerical linear algebra analogs of the iterative methods covered in the book are discussed. Its standard application to the convergence theory of multilevel and domain decomposition methods for solving PDE problems is explained, and links to optimization theory and online learning algorithms are given. Providing an introduction and overview of iterative methods which are based on problem decompositions and suitable for parallel and distributed computing, the book could serve as the basis for a one- or two-semester course for M.S. and Ph.D. students specializing in numerical analysis and scientific computing. It will also appeal to a wide range of researchers interested in scientific computing in the broadest sense.

Iterative Methods For Sparse Linear Systems

DOWNLOAD
Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01

Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.

Mathematics of Computing -- General.

New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations

DOWNLOAD
Author : Jacques Tagoudjeu
language : en
Publisher: Universal-Publishers
Release Date : 2011-04

New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04 with Mathematics categories.

This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.

Augmented Lagrangian And Operator Splitting Methods In Nonlinear Mechanics

DOWNLOAD
Author : Ronald Glowinski
language : en
Publisher: SIAM
Release Date : 1989-01-01

Augmented Lagrangian And Operator Splitting Methods In Nonlinear Mechanics written by Ronald Glowinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Science categories.

A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator-splitting methods such as alternating-methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite-element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods additionally used to study them. These ideas are then applied to specific classes of mechanical problems.

Splitting Algorithms Modern Operator Theory And Applications

DOWNLOAD
Author : Heinz H. Bauschke
language : en
Publisher: Springer Nature
Release Date : 2019-11-06

Splitting Algorithms Modern Operator Theory And Applications written by Heinz H. Bauschke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-06 with Mathematics categories.

This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.

Multiscale Wavelet Methods For Partial Differential Equations

DOWNLOAD
Author : Wolfgang Dahmen
language : en
Publisher: Elsevier
Release Date : 1997-08-13

Multiscale Wavelet Methods For Partial Differential Equations written by Wolfgang Dahmen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-13 with Mathematics categories.

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. - Covers important areas of computational mechanics such as elasticity and computational fluid dynamics - Includes a clear study of turbulence modeling - Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations - Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications

The Krasnosel Ski Mann Iterative Method

DOWNLOAD
Author : Qiao-Li Dong
language : en
Publisher: Springer Nature
Release Date : 2022-02-24

The Krasnosel Ski Mann Iterative Method written by Qiao-Li Dong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-24 with Mathematics categories.

This brief explores the Krasnosel'skiĭ-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

Additive Operator Difference Schemes

DOWNLOAD
Author : Petr N. Vabishchevich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-11-27

Additive Operator Difference Schemes written by Petr N. Vabishchevich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.

Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.

Domain Decomposition Methods In Scientific And Engineering Computing

DOWNLOAD
Author : David E. Keyes
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Domain Decomposition Methods In Scientific And Engineering Computing written by David E. Keyes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term ``domain decomposition'' has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with so-called ``bad parameters'' in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the elliptically-dominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an up-to-date guide to the many facets of the theory and practice of domain decomposition.

Functional Analysis Methods In Numerical Analysis

DOWNLOAD
Author : M. Z. Nashed
language : en
Publisher: Springer
Release Date : 2006-11-15

Functional Analysis Methods In Numerical Analysis written by M. Z. Nashed and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.