Computing eigenvalues of quasi‐rational Bernstein–Vandermonde matrices to high relative accuracy

Abstract

AbstractIn this article, we consider how to accurately solve the eigenvalue problem for a class of quasi‐rational Bernstein–Vandermonde (q‐RBV) matrices. This class of matrices belongs to generalized sign regular matrices with signature . An algorithm is developed to accurately compute the parameter matrix for q‐RBV matrices. Based on the parameter matrix, all the eigenvalues of q‐RBV matrices have been computed to high relative accuracy. The perturbation theory for the eigenvalues of q‐RBV matrices and the error analysis of our proposed algorithm are provided. Numerical experiments are performed to confirm the claimed high relative accuracy.