An Optimal Least-Square Solver For Scaled Partial-Isometric Linear Systems

TL;DR

This paper introduces an efficient $O(mn)$ direct least-squares solver tailored for scaled partial-isometric linear systems, including block diagonal cases, with numerical experiments demonstrating its effectiveness.

Contribution

The paper presents a novel $O(mn)$ direct solver specifically designed for scaled partial-isometric systems, expanding applicability to block diagonal cases with different scales.

Findings

Solver operates in $O(mn)$ time complexity.

Effective for block diagonal systems with distinct scales.

Numerical experiments confirm practical efficiency.

Abstract

We present an $O(mn)$ direct least-squares solver for $m \times n$ linear systems with a scaled partial isometry. The proposed algorithm is also useful when the system is block diagonal and each block is a scaled partial isometry with distinct scaling factors. We also include numerical experiments as a demonstration.