Krylov Methods For Nonsymmetric Linear Systems PDF Download
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Author | : Gérard Meurant |
Publisher | : Springer Nature |
Total Pages | : 686 |
Release | : 2020-10-02 |
Genre | : Mathematics |
ISBN | : 3030552519 |
Download Krylov Methods for Nonsymmetric Linear Systems Book in PDF, ePub and Kindle
This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.
Author | : Yousef Saad |
Publisher | : SIAM |
Total Pages | : 537 |
Release | : 2003-04-01 |
Genre | : Mathematics |
ISBN | : 0898715342 |
Download Iterative Methods for Sparse Linear Systems Book in PDF, ePub and Kindle
Mathematics of Computing -- General.
Author | : Tracy L. Ewen |
Publisher | : |
Total Pages | : 0 |
Release | : 2000 |
Genre | : |
ISBN | : |
Download Mixed Product Krylov Subspace Methods for Solving Nonsymmetric Linear Systems Book in PDF, ePub and Kindle
Author | : H. A. van der Vorst |
Publisher | : Cambridge University Press |
Total Pages | : 242 |
Release | : 2003-04-17 |
Genre | : Mathematics |
ISBN | : 9780521818285 |
Download Iterative Krylov Methods for Large Linear Systems Book in PDF, ePub and Kindle
Table of contents
Author | : Y. Saad |
Publisher | : |
Total Pages | : 52 |
Release | : 1981 |
Genre | : Conjugate gradient methods |
ISBN | : |
Download Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems Book in PDF, ePub and Kindle
Author | : Anthony Chronopoulos |
Publisher | : |
Total Pages | : 28 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download Krylov Subspace Iterative Methods for Nonsymmetric Indefinite Linear Systems Book in PDF, ePub and Kindle
Author | : Steven Lewis Lee |
Publisher | : |
Total Pages | : 292 |
Release | : 1993 |
Genre | : |
ISBN | : |
Download Krylov Methods for the Numerical Solution of Initial-value Problems in Differential Algebraic Equations Book in PDF, ePub and Kindle
Author | : Tony F. Chan |
Publisher | : |
Total Pages | : 13 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download A Mixed Product Krylov Subspace Method for Solving Nonsymmetric Linear Systems Book in PDF, ePub and Kindle
Author | : Marko Huhtanen |
Publisher | : |
Total Pages | : 13 |
Release | : 1996 |
Genre | : |
ISBN | : 9789512230754 |
Download Krylov Subspace Methods of EN Type for a Nonsymmetric Linear System and Its Spectrum Book in PDF, ePub and Kindle
Author | : H. C. Elman |
Publisher | : |
Total Pages | : 23 |
Release | : 1984 |
Genre | : |
ISBN | : |
Download A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations Book in PDF, ePub and Kindle
This document presents an iterative method for solving large sparse nonsymmetric linear systems of equations that enhances Manteuffel's adaptive Chebyshev method with a conjugate gradient-like method. The new method replaces the modified power method for computing needed eigenvalue estimates with Arnoldi's method, which can be used to simultaneously compute eigenvalues and to improve the approximate solution. Convergence analysis and numerical experiments suggest that the method is more efficient than the original adaptive Chebyshev algorithm. (Author).