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Flexible Modified LSMR Method for Least Squares Problems

Numerical Analysis 2024-08-30 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2408.16652,
  title  = {Flexible Modified LSMR Method for Least Squares Problems},
  author = {Mei Yang and Gul Karaduman and Ren-Cang Li},
  journal= {arXiv preprint arXiv:2408.16652},
  year   = {2024}
}

Comments

19 pages, 2 figures

R2 v1 2026-06-28T18:27:51.800Z