Work

Flexible modified LSMR for least squares problems

Year: 2025

Type: article

Abstract: LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these preconditioning techniques is the need to solve two linear systems per iterative step. In this paper, to tackle this issue, among others, a modified LSMR method (MLSMR), in which only one linear system per iterative step needs to be solved instead of two, is introduced, and then it is integrated with the idea of flexible GMRES to yield a flexible MLSMR method (FMLSMR). Numerical examples are presented to demonstrate the efficiency of the proposed FMLSMR method.

Source: Numerical Algebra Control and Optimization

DOI: 10.3934/naco.2025019

Authors: Mei Yang, Gul Karaduman, Ren-Cang Li

Institutions: The University of Texas at Arlington, Karamanoğlu Mehmetbey University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Self-supervised Probabilistic Graph Structure Learning for Task-agnostic Latent Representation