The Lanczos And Conjugate Gradient Algorithms

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The Lanczos And Conjugate Gradient Algorithms

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Author : Gerard Meurant
language : en
Publisher: SIAM
Release Date : 2006-08-01

The Lanczos And Conjugate Gradient Algorithms written by Gerard Meurant and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-01 with Computers categories.

The most comprehensive and up-to-date discussion available of the Lanczos and CG methods for computing eigenvalues and solving linear systems.

The Lanczos And Conjugate Gradient Algorithms

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Author : Gerard Meurant
language : en
Publisher: SIAM
Release Date : 2006-01-01

The Lanczos And Conjugate Gradient Algorithms written by Gerard Meurant and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Computers categories.

The Lanczos and conjugate gradient (CG) algorithms are fascinating numerical algorithms. This book presents the most comprehensive discussion to date of the use of these methods for computing eigenvalues and solving linear systems in both exact and floating point arithmetic. The author synthesizes the research done over the past 30 years, describing and explaining the "average" behavior of these methods and providing new insight into their properties in finite precision. Many examples are given that show significant results obtained by researchers in the field. The author emphasizes how both algorithms can be used efficiently in finite precision arithmetic, regardless of the growth of rounding errors that occurs. He details the mathematical properties of both algorithms and demonstrates how the CG algorithm is derived from the Lanczos algorithm. Loss of orthogonality involved with using the Lanczos algorithm, ways to improve the maximum attainable accuracy of CG computations, and what modifications need to be made when the CG method is used with a preconditioner are addressed.

Linear And Nonlinear Conjugate Gradient Related Methods

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Author : Loyce M. Adams
language : en
Publisher: SIAM
Release Date : 1996-01-01

Linear And Nonlinear Conjugate Gradient Related Methods written by Loyce M. Adams and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.

Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.

Error Norm Estimation In The Conjugate Gradient Algorithm

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Author : Gérard Meurant
language : en
Publisher: SIAM
Release Date : 2024-01-30

Error Norm Estimation In The Conjugate Gradient Algorithm written by Gérard Meurant and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-30 with Mathematics categories.

The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.

Conjugate Gradient Algorithms And Finite Element Methods

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Author : M. Křížek
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-11

Conjugate Gradient Algorithms And Finite Element Methods written by M. Křížek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-11 with Computers categories.

The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.

The Symmetric Eigenvalue Problem

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Author : Beresford N. Parlett
language : en
Publisher: SIAM
Release Date : 1980-01-01

The Symmetric Eigenvalue Problem written by Beresford N. Parlett and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.

Mathematics of Computing -- Numerical Analysis.

Matrices Moments And Quadrature With Applications

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Author : Gene H. Golub
language : en
Publisher: Princeton University Press
Release Date : 2009-12-07

Matrices Moments And Quadrature With Applications written by Gene H. Golub and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-07 with Mathematics categories.

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Iterative Methods For Sparse Linear Systems

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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.

The Lanczos Method

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Author : Louis Komzsik
language : en
Publisher: SIAM
Release Date : 2003-01-01

The Lanczos Method written by Louis Komzsik and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.

A valuable reference on the Lanczos method for graduate numerical analysts and engineers.

Mathematical Programming The State Of The Art

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Author : A. Bachem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematical Programming The State Of The Art written by A. Bachem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.