What question did this study set out to answer?

This research focuses on developing and analyzing two block Gauss-Seidel methods for efficient solutions to large linear least squares problems.

June 28, 2026

On Fast Randomized and Deterministic Block Gauss‐Seidel Methods for Solving Least Squares Problems

Key Points

This research focuses on developing and analyzing two block Gauss-Seidel methods for efficient solutions to large linear least squares problems.
Development of both randomized and deterministic block Gauss-Seidel methods.
Proof of convergence for full-rank overdetermined systems.
Conducting numerical experiments to validate effectiveness against existing methods.
The proposed methods showed superior effectiveness when applied to large linear least squares problems.
Convergence was successfully proven for the methods in full-rank overdetermined systems.
Numerical tests indicated enhanced implementation advantages compared to block Kaczmarz and block coordinate descent algorithms.

Abstract

ABSTRACT In this paper, we propose and analyze two block Gauss‐Seidel methods, one randomized and one deterministic, to solve large linear least squares problems. We prove the convergence of the proposed methods for full‐rank overdetermined systems and provide numerical experiments to show their effectiveness compared to existing methods. In contrast to other block Kaczmarz and block coordinate descent algorithms, the proposed methods are especially advantageous when it comes to their implementation.

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