Work

A Rational Arnoldi Approach for Sobolev Rational Least Squares Problems

Year: 2025

Type: article

Abstract: ABSTRACT In this article, we propose a rational Arnoldi‐based algorithm for solving Sobolev rational least squares problems. The classical approach to tackle least squares problems is to solve a system with a Vandermonde‐type coefficient matrix. Unfortunately, even for modest sizes, the ill‐conditioning of the coefficient matrix does not typically allow for accurate numerical computations. To overcome this drawback we exploit the link between the coefficient matrix and (rational) Krylov subspaces. We extend the theory by allowing the Krylov space to be generated not only by a diagonal matrix, but also by Jordan matrices, which links back to least squares problems involving approximations of the derivatives as well. This allows us to tackle Sobolev polynomial and Sobolev rational least squares problems. Examples are provided to illustrate the performance of the proposed approach.

Source: Numerical Linear Algebra with Applications

DOI: 10.1002/nla.70017

Authors: Amin Faghih, Marc Van Barel, Niel Van Buggenhout, Raf Vandebril

Institutions: KU Leuven, Universidad Carlos III de Madrid

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: Fonds Wetenschappelijk Onderzoek, KU Leuven, Vlaamse regering

Awards: ManiFactor: Factor analysis for maps into manifolds, G2512920741, Low rank tensor approximation techniques for up- and downdating of massive online time series clustering, Short recurrence relations for rational Krylov and orthogonal rational functions inspired by modified moments