Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:2-1-4
Session:
Number:2-1-4-4
Numerical Verification Method for Dense Linear Systems with Arbitrarily Ill-conditioned Matrices
Takahisa OHTA, Takeshi OGITA, Siegfried M. Rump, Shin’ichi OISHI,
pp.745-748
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
This paper is concerned with the problem of verifying an accuracy of a computed solution of linear systems with an arbitrarily ill-conditioned coefficient matrix. In this paper, a method of obtaining an accurate computed solution of such linear systems and its verified error bound is proposed. The proposed method is based on the accurate computation of dot product and IEEE standard 754 arithmetic. A verified and accurate computed solution with a desired tolerance can be obtained by the proposed method with iterative refinement. Numerical results are presented for illustrating the effectiveness of the proposed method.