Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices

TL;DR

This paper presents efficient parallel three-level J-Jacobi algorithms for Hermitian matrices, achieving load balancing and cache optimization, suitable for diverse modern architectures, with accurate eigenvalue computation.

Contribution

It introduces novel parallel blocking techniques for J-Jacobi algorithms that enhance load balancing and cache efficiency across various hardware architectures.

Findings

Achieves near-ideal load balancing across processors.

Utilizes blocking to exploit local cache memory.

Maintains high relative accuracy in eigenvalue computations.

Abstract

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal load balancing between all available processors/cores is obtained. A similar blocking technique can be used to exploit local cache memory of each processor to further speed up the process. Due to diversity of modern computer architectures, each of the algorithms described here may be the method of choice for a particular hardware and a given matrix size. All proposed block algorithms compute the eigenvalues with relative accuracy similar to the original non-blocked Jacobi algorithm.