Computing eigenvalues of quasi-rational Said–Ball–Vandermonde matrices

Abstract

This paper focuses on computing the eigenvalues of the generalized collocation matrix of the rational Said–Ball basis, also called as the quasi-rational Said–Ball–Vandermonde (q-RSBV) matrix, with high relative accuracy. To achieve this, we propose explicit expressions for the minors of the q-RSBV matrix and develop a high-precision algorithm to compute these parameters. Additionally, we present perturbation theory and error analysis to further analyze the accuracy of our approach. Finally, we provide some numerical examples to demonstrate the high relative accuracy of our algorithms.