A Hybrid Algorithm for Computing a Partial Singular Value Decomposition Satisfying a Given Threshold

TL;DR

This paper introduces a hybrid algorithm for efficiently computing singular triplets above a threshold, with implementations in MATLAB/Octave and R, demonstrated through applications like matrix completion and image compression.

Contribution

A novel hybrid algorithm for partial SVD computation above a threshold, with accessible MATLAB/Octave and R implementations and demonstrated practical applications.

Findings

High performance in numerical examples

Ease of use in various applications

Publicly available well-documented codes

Abstract

In this paper, we describe a new hybrid algorithm for computing all singular triplets above a given threshold and provide its implementation in MATLAB/Octave and R. The high performance of our codes and ease at which they can be used, either independently or within a larger numerical scheme, are illustrated through several numerical examples with applications to matrix completion and image compression. Well-documented MATLAB and R codes are provided for public use.