Super-fast validated solution of linear systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:199

Article; Proceedings Paper

Rump, Siegfried M. ; Ogita, Takeshi

关键词: self-validating methods;    verified error bounds;    sparse linear systems;    INTLAB;   

DOI  :  10.1016/j.cam.2005.07.038

来源: Elsevier

【 摘 要 】

Validated solution of a problem means to compute error bounds for a solution in finite precision. This includes the proof of existence of a solution. The computed error hounds are to be correct including all possible effects of rounding errors. The fastest known validation algorithm for the solution of a system of linear equations requires twice the computing time of a standard (purely) numerical algorithm. In this paper we present a super-fast validation algorithm for linear systems with symmetric positive definite matrix. This means that the entire computing time for the validation algorithm including computation of an approximated solution is the same as for a standard numerical algorithm. Numerical results are presented. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free