A randomized algorithm for the QR decomposition-based approximate SVD

TL;DR

This paper introduces a new randomized algorithm for approximate SVD based on QR decomposition, improving speed and accuracy over existing methods, with verified numerical experiments and error estimates.

Contribution

The paper presents a novel randomized approximate SVD algorithm utilizing QR decomposition, addressing classical SVD bottlenecks with competitive convergence and error bounds.

Findings

Achieves satisfactory convergence speed and accuracy

Provides an estimate for Frobenius norm approximation error

Numerical experiments verify the algorithm's effectiveness

Abstract

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on Qatar Riyal decomposition (RCSVD-QR). Our method utilize random sampling and the OR decomposition to address a serious bottlenck associated with classical SVD. RCSVD-QR gives satisfactory convergence speed as well as accuracy as compared to those state-of-the-art algorithms. In addition, we provides an estimate for the expected approximation error in Frobenius norm. Numerical experiments verify these claims.