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Iterative Incomplete Factorization Methods
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Book Synopsis Iterative Incomplete Factorization Methods by : Valeri? Pavlovich Il?in
Download or read book Iterative Incomplete Factorization Methods written by Valeri? Pavlovich Il?in and published by World Scientific. This book was released on 1992 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to numerical methods for solving sparse linear algebra systems of very large dimension which arise in the implementation of the mesh approximations of the partial differential equations. Incomplete factorization is the basis of the wide class of preconditioning interative processes with acceleration by conjugate gradients or the Chebyshev technique. Different kinds of explicit and implicit algorithms are considered. Theoretical grounds of correctness and estimates of the convergence velocity of iterations are presented. Together with the results of experimental investigations for the typical examples, this book is the first on systematic studying of the incomplete factorization methods.
Book Synopsis Iterative Solution Methods by : Owe Axelsson
Download or read book Iterative Solution Methods written by Owe Axelsson and published by Cambridge University Press. This book was released on 1996-03-29 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.
Book Synopsis Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by : Daniele Bertaccini
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Book Synopsis Local Mode Smoothing Analysis of Various Incomplete Factorization Iterative Methods in Two Dimensions by : M. Khalil
Download or read book Local Mode Smoothing Analysis of Various Incomplete Factorization Iterative Methods in Two Dimensions written by M. Khalil and published by . This book was released on 1989 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Krylov Methods for Large Linear Systems by : H. A. van der Vorst
Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Parallel Numerical Algorithms by : David E. Keyes
Download or read book Parallel Numerical Algorithms written by David E. Keyes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.
Book Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset
Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
Book Synopsis Iterative Solution of Symmetric Quasi-definite Linear Systems by : Dominique Orban
Download or read book Iterative Solution of Symmetric Quasi-definite Linear Systems written by Dominique Orban and published by SIAM. This book was released on 2017-04-07 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure.? This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia.? The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.?
Book Synopsis Local Mode Smoothing Analysis for Various Incomplete Factorization Iterative Methods in Three Dimensions by : M. Khalil
Download or read book Local Mode Smoothing Analysis for Various Incomplete Factorization Iterative Methods in Three Dimensions written by M. Khalil and published by . This book was released on 1989 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset
Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
Book Synopsis Templates for the Solution of Linear Systems by : Richard Barrett
Download or read book Templates for the Solution of Linear Systems written by Richard Barrett and published by SIAM. This book was released on 1994-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Book Synopsis Local Mode Smoothing Analysis of Various Two-dimensional Incomplete Factorization by : M. Khalil
Download or read book Local Mode Smoothing Analysis of Various Two-dimensional Incomplete Factorization written by M. Khalil and published by . This book was released on 1988 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Incomplete Factorization Preconditioning for Linear Least Squares Problems by : Xiaoge Wang
Download or read book Incomplete Factorization Preconditioning for Linear Least Squares Problems written by Xiaoge Wang and published by . This book was released on 1993 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: When certain conditions are imposed on the sparsity pattern of the preconditioning matrix, incomplete Cholesky (IC) factorization is identical to IMGS. Therefore, a sufficient condition on the sparsity pattern for a stable IC factorization can be derived. Based on this condition, three algorithms for modifying a sparsity pattern for which IC may not succeed have been designed. These methods differ from previously proposed methods to guarantee the existence and improve the stability of the IC factorization since they do not require numerical information. Numerical experiments illustrating the capabilities of the preconditioners are also presented."
Book Synopsis Algorithms for Sparse Linear Systems by : Jennifer Scott
Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.
Book Synopsis An Automatic Ordering Method for Incomplete Factorization Iterative Solvers by : University of Waterloo. Dept. of Computer Science
Download or read book An Automatic Ordering Method for Incomplete Factorization Iterative Solvers written by University of Waterloo. Dept. of Computer Science and published by . This book was released on 1990 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Use of Iterative Methods and Blocking for Solving Sparse Triangular Systems in Incomplete Factorization Preconditioning by :
Download or read book On the Use of Iterative Methods and Blocking for Solving Sparse Triangular Systems in Incomplete Factorization Preconditioning written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
