Error Norm Estimation in the Conjugate Gradient Algorithm

Download or read book Error Norm Estimation in the Conjugate Gradient Algorithm written by Gérard Meurant and published by SIAM. This book was released on 2024-01-30 with total page 138 pages. 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.