A generalized Nystrom method with column sketching for low-rank approximation of nonsymmetric matrices

TL;DR

This paper introduces a generalized Nystrom method with column sketching for efficient and accurate low-rank approximation of large-scale nonsymmetric matrices, extending classical techniques to broader applications.

Contribution

It extends the classical Nystrom method to nonsymmetric matrices using column sketching, improving accuracy and speed while maintaining stability.

Findings

Demonstrates robustness in numerical experiments

Achieves better accuracy compared to existing methods

Provides faster computation for large matrices

Abstract

This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite matrices, we explore an extension of the Nystrom method to approximate nonsymmetric matrices. The proposed method is a generalized Nystrom method with column sketching and shows its advantages in accuracy and speed without sacri cing stability. And the numerical experiments will illustrate the robustness of our new methods in finding a desired low-rank approximation of nonsymmetric matrix.