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Error Norm Estimation in the Conjugate Gradient Algorithm

2024 Algorithms
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Release : 2024
Genre : Algorithms
Kind : eBook
Book Rating : 851/5 ( reviews)

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Book Synopsis Error Norm Estimation in the Conjugate Gradient Algorithm by : Gérard A. Meurant

Download or read book Error Norm Estimation in the Conjugate Gradient Algorithm written by Gérard A. Meurant. This book was released on 2024. Available in PDF, EPUB and Kindle. Book excerpt: "Describes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error and analyzes them"--

Error Norm Estimation in the Conjugate Gradient Algorithm

2024-01-30 Mathematics
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Release : 2024-01-30
Genre : Mathematics
Kind : eBook
Book Rating : 86X/5 ( reviews)

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Book Synopsis Error Norm Estimation in the Conjugate Gradient Algorithm by : Gérard Meurant

Download or read book Error Norm Estimation in the Conjugate Gradient Algorithm written by Gérard Meurant . This book was released on 2024-01-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations

2003
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Release : 2003
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations by : Owe Axelsson

Download or read book Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations written by Owe Axelsson. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:

Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations

2000
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Release : 2000
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Book Synopsis Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations by : Owe Axelsson

Download or read book Error Norm Estimation and Stopping Criteria in Preconditioned Conjugate Gradient Iterations written by Owe Axelsson. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:

Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs

2014-12-22 Mathematics
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Release : 2014-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 83X/5 ( reviews)

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Book Synopsis Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs by : Josef Malek

Download or read book Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs written by Josef Malek. This book was released on 2014-12-22. Available in PDF, EPUB and Kindle. Book excerpt: Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?

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