Fast verification of solutions for sparse monotone matrix equations

Takeshi Ogita, Shin'ichi Oishi, Yasunori Ushiro

published in
Topics in Numerical Analysis: With Special Emphasis on Nonlinear Problems
(Computing, Supplement 15, G. Alefeld and X. Chen eds.), pp. 175-187, Springer WienNewYork, Austria, 2001.

Abstract
This paper concerns the problem of verifying the accuracy of a numerical solution for linear systems with a coefficient matrix being sparse and monotone. Fast algorithms calculate a verified error bound for numerical solutions of the linear systems and a guaranteed condition number of the coefficient matrix. The proposed verification method is based on iterative solution methods and rounding mode controlled computations. Numerical results have also been presented for illustrating that a cost for verification is less than that for calculating a numerical solution.