Fast verification of solutions for sparse monotone matrix equations
Takeshi Ogita, Shin'ichi Oishi, Yasunori Ushiro
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.
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.