Two-sided uniformly randomized GSVD for large-scale discrete ill-posed problems with Tikhonov regularizations

TL;DR

This paper introduces a two-sided randomized GSVD algorithm that efficiently solves large-scale discrete ill-posed problems with Tikhonov regularization, reducing computational costs while maintaining accuracy.

Contribution

The paper presents a novel two-sided uniform randomized GSVD method tailored for large-scale ill-posed problems with Tikhonov regularization, improving efficiency and accuracy.

Findings

Reduced computational time and memory usage.

Achieved expected accuracy in numerical experiments.

Error analysis supports the method's reliability.

Abstract

The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algorithm for solving the large-scale discrete ill-posed problem with the general Tikhonov regularization. Based on two-sided uniform random sampling, the proposed algorithm can improve the efficiency with less computing time and memory requirement and obtain expected accuracy. The error analysis for the proposed algorithm is also derived. Finally, we report some numerical examples to illustrate the efficiency of the proposed algorithm.