前処理によるBarnettの定理に基づく近似GCD計算の安定化の検討

Abstract

In this paper, we consider stabilizing the approximate GCD computation by Barnett's theorem by preprocessing the Bezout matrix. As preprocessing methods, we discuss numerical matrix construction methods and the removal of unstable elements/rows of matrix that are over-determined systems, using many numerical examples. The condition number is one measure of numerical instability that is algorithm-independent, but there are several algorithm-specific measures. In this paper, we also discuss the conversion to a dominant-diagonal matrix, which is a convergence condition for the Gauss- Seidel method and the Jacobi method.