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portada Error Norm Estimation in the Conjugate Gradient Algorithm
Type
Physical Book
Publisher
Author
Collection
SIAM Spotlights
Year
2024
Language
English
Pages
127
Format
Paperback
ISBN13
9781611977851

Error Norm Estimation in the Conjugate Gradient Algorithm

Gérard Meurant;Petr Tichý (Author) · SIAM - Society for Industrial and Applied Mathematics · Paperback

Error Norm Estimation in the Conjugate Gradient Algorithm - Gérard Meurant;Petr Tichý

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Synopsis "Error Norm Estimation in the Conjugate Gradient Algorithm"

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 analyses 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.

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. Computation of 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.

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