A mixed precision Jacobi SVD algorithm

TL;DR

This paper introduces a mixed precision Jacobi SVD algorithm that accelerates computation by combining lower and higher precision calculations, achieving about twice the speed of traditional methods without losing accuracy.

Contribution

The paper presents a novel mixed precision Jacobi SVD algorithm that improves speed while maintaining accuracy through a two-step process involving preconditioning and iterative refinement.

Findings

Achieves approximately 2x speedup on x86-64 architecture.

Maintains high accuracy comparable to traditional algorithms.

Effectively combines lower and higher precision computations.

Abstract

We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and then performs one-sided Jacobi rotations in the working precision as iterative refinement. By carefully transforming a lower precision solution to a higher precision one, our algorithm achieves about 2 times speedup on the x86-64 architecture compared to the usual one-sided Jacobi SVD algorithm in LAPACK, without sacrificing the accuracy.