対称正定値疎行列の条件数概算法

抄録

In this paper, we study the method of roughly computing the condition number of a symmetric positive definite sparse matrix. The estimation of the condition number of a matrix relative to inversion is important for bounding the errors in computer solutions of a linear system of equations. We give an easy and fast algorithm based on power method and inverse iteration method using Preconditioned Conjugate Gradient method. This algorithm is applicable for large scale problems, and the computing time of the condition number is less than five times the computing time of solving given equations Ax=b using PCG method.