Accurate computations of eigenvalues of quasi-Cauchy-Vandermonde matrices

Abstract

In this paper, we consider the eigenvalue problem for the class of quasi-Cauchy-Vandermonde (qCV) matrices belonging to the class of generalized sign regular matrices with signature (1,…,1,−1). We present the explicit expressions of minors of qCV matrices. An algorithm is designed to accurately compute the parameterization matrix for qCV matrices. Based on the parameterization matrix, all the eigenvalues of such matrices are computed to high relative accuracy. Error analysis and numerical experiments are presented to confirm the high relative accuracy.