On Truncated-SVD-like Sparse Solutions to Least-Squares Problems of Arbitrary Dimensions

TL;DR

This paper introduces two algorithms for finding sparse solutions to least-squares problems with arbitrary dimensions, demonstrating their solutions are close to those obtained by truncated SVD, thus offering efficient alternatives.

Contribution

The paper presents novel algorithms for sparse least-squares solutions applicable to arbitrary dimensions, extending the truncated SVD approach with provable closeness.

Findings

Algorithms produce solutions close to truncated SVD results

Applicable to arbitrary-dimensional coefficient matrices

Efficient computation of sparse solutions

Abstract

We describe two algorithms for computing a sparse solution to a least-squares problem where the coefficient matrix can have arbitrary dimensions. We show that the solution vector obtained by our algorithms is close to the solution vector obtained via the truncated SVD approach.