Randomized dual singular value decomposition

TL;DR

This paper introduces a randomized dual singular value decomposition method that reduces computational costs while maintaining accuracy, supported by theoretical analysis and numerical experiments.

Contribution

It presents a novel randomized approach to dual SVD, offering efficiency improvements over traditional methods.

Findings

Significant reduction in computational cost.

Maintains similar accuracy to classical dual SVD.

Theoretical analysis supports the effectiveness of the randomized method.

Abstract

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze the theoretical properties and illuminate the numerical performance of the randomized algorithm.