Author: Gérard Meurant
Publisher: Springer Nature
ISBN: 3030552519
Category : Mathematics
Languages : en
Pages : 686
Book Description
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with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms.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.
Krylov Methods for Nonsymmetric Linear Systems
Author: Gérard Meurant
Publisher: Springer Nature
ISBN: 3030552519
Category : Mathematics
Languages : en
Pages : 686
Book Description
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.
Publisher: Springer Nature
ISBN: 3030552519
Category : Mathematics
Languages : en
Pages : 686
Book Description
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.
Mixed Product Krylov Subspace Methods for Solving Nonsymmetric Linear Systems
Author: Tracy L. Ewen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Iterative Methods for Sparse Linear Systems
Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
Book Description
Mathematics of Computing -- General.
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
Book Description
Mathematics of Computing -- General.
Iterative Krylov Methods for Large Linear Systems
Author: H. A. van der Vorst
Publisher: Cambridge University Press
ISBN: 9780521818285
Category : Mathematics
Languages : en
Pages : 242
Book Description
Table of contents
Publisher: Cambridge University Press
ISBN: 9780521818285
Category : Mathematics
Languages : en
Pages : 242
Book Description
Table of contents
Krylov Subspace Iterative Methods for Nonsymmetric Indefinite Linear Systems
Author: Anthony Chronopoulos
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
Book Description
A Mixed Product Krylov Subspace Method for Solving Nonsymmetric Linear Systems
Author: Tony F. Chan
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
Book Description
Solving Linear Systems on Vector and Shared Memory Computers
Author: J. J. Dongarra
Publisher: Society for Industrial and Applied Mathematics (SIAM)
ISBN:
Category : Computers
Languages : en
Pages : 274
Book Description
Mathematics of Computing -- Parallelism.
Publisher: Society for Industrial and Applied Mathematics (SIAM)
ISBN:
Category : Computers
Languages : en
Pages : 274
Book Description
Mathematics of Computing -- Parallelism.
Krylov Subspace Methods of EN Type for a Nonsymmetric Linear System and Its Spectrum
Author: Marko Huhtanen
Publisher:
ISBN: 9789512230754
Category :
Languages : en
Pages : 13
Book Description
Publisher:
ISBN: 9789512230754
Category :
Languages : en
Pages : 13
Book Description
A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations
Author: H. C. Elman
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
Book Description
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).
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
Book Description
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).
On Squaring Krylov Subspace Iterative Methods for Nonsymmetric Linear System
Author: Anthony Chronopoulos
Publisher:
ISBN:
Category : Iterative methods (Mathematics)
Languages : en
Pages : 31
Book Description
Abstract: "The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gradients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orthodir(2) methods. We make theoretical and experimental comparisons."
Publisher:
ISBN:
Category : Iterative methods (Mathematics)
Languages : en
Pages : 31
Book Description
Abstract: "The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gradients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orthodir(2) methods. We make theoretical and experimental comparisons."