Advances on the recovery of (perturbed) Cauchy matrices

TL;DR

This paper introduces new algorithms and error estimates for efficiently recovering the generators of (perturbed) Cauchy matrices, with a displacement-based approach showing improved accuracy in numerical experiments.

Contribution

It presents a general family of algorithms for Cauchy parameter recovery, including a novel displacement-based method with enhanced accuracy.

Findings

Displacement-based algorithm outperforms previous methods in accuracy.

New error estimates improve understanding of algorithm performance.

Numerical experiments validate the effectiveness of the proposed algorithms.

Abstract

Given a (possibly approximate) Cauchy matrix, how can we efficiently compute its generators? Expanding on previous work by Liesen and Luce [Linear Algebra Appl. 493 (2016) 261--280], we present a general family of algorithms for Cauchy parameter recovery, together with new error estimates. We also introduce a displacement-based approximation, which leads to a new algorithm for Cauchy parameter recovery. Numerical experiments show that the algorithm based on the displacement approximation is generally more accurate than the other algorithms.