An iterative method with error estimators

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:127

Article

Calvetti, D ; Morigi, S ; Reichel, L ; Sgallari, F

关键词: Lanczos process;    conjugate gradient method;    symmetric linear system;    Gauss quadrature;   

DOI  :  10.1016/S0377-0427(00)00494-5

来源: Elsevier

【 摘 要 】

Iterative methods for the solution of linear systems of equations produce a sequence of approximate solutions. In many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small. This paper presents a new iterative method based on the Lanczos process for the solution of linear systems of equations with a symmetric matrix. The method is designed to allow the computation of estimates of the Euclidean norm of the error in the computed approximate solutions. These estimates are determined by evaluating certain Gauss, anti-Gauss, or Gauss-Radau quadrature rules. (C) 2001 Elsevier Science B.V. All rights reserved.

【 授权许可】

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