悪条件連立一次方程式の精度保証付き数値計算法(計算の品質, <特集>平成17年研究部会連合発表会)

抄録

This paper is concerned with the problem of verifying an accuracy of a numerical solution of a linear system with an arbitrarily ill-conditioned coefficient matrix. In this paper, a method of obtaining an accurate numerical solution of such a linear system 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 numerical 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.