Numerical Verification for Each Eigenvalues of Symmetric Matrix(Quality of Computations, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

A fast verification method of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a negligible additional cost. Finally this paper includes some numerical examples to show the efficiency of the proposed method.