Methods Obtaining Accurate Numerical Solutions for Linear Systems Based on Verified Numerical Computations

Abstract

Abstract. Several verification methods have been proposed for linear systems. The verification methods first produce an approximate solution, and next provide its error bound. In this paper, we first set a criterion for an error bound, and next propose a numerical method that produces an approximate solution satisfying the criterion. The criterion is faithful rounding, floating-point neighbors, or rounding to nearest.