Efficient Solution of Parameter Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions

TL;DR

This paper introduces an efficient, structure-preserving algorithm for solving parameter-dependent quasiseparable systems and computing matrix functions, demonstrating speed and robustness through numerical experiments.

Contribution

It develops a novel algorithm that exploits quasiseparable structure invariance under shifts and inversions for faster, more stable matrix computations.

Findings

Algorithm is faster than existing methods.

Method maintains numerical stability.

Effective for computing various matrix functions.

Abstract

In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the quasiseparable structure under diagonal shifting and inversion. This algorithm is applied to compute various functions of matrices. Numerical experiments show that this approach is fast and numerically robust.