Mixed precision thin SVD algorithms based on the Gram matrix

TL;DR

This paper introduces a mixed precision thin SVD algorithm that uses the Gram matrix and Jacobi methods, achieving high accuracy and significant speedups over traditional methods on various computing systems.

Contribution

The paper presents a novel mixed precision algorithm for thin SVD that combines Gram matrix construction and Jacobi methods, improving accuracy and computational efficiency.

Findings

Attains high relative accuracy in singular values.

Achieves over 10x speedup on a single CPU.

Provides about 2x speedup on distributed systems.

Abstract

In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and coupling it with a Jacobi algorithm, our theoretical analysis and numerical experiments both indicate that the singular values computed by this mixed precision thin SVD algorithm attain high relative accuracy. In practice, our mixed precision thin SVD algorithm yields speedups of over 10x on a single CPU and about 2x on distributed memory systems when compared with traditional thin SVD methods.