Performance of the Block Jacobi Method for the Symmetric Eigenvalue Problem on a Modern Massively Parallel Computer∗

A Parallel Performance Study of Jacobi-like Eigenvalue Solution

In this report we focus on Jacobi like resolution of the eigen-problem for a real symmetric matrix from a parallel performance point of view: we try to optimize the algorithm working on the communication intensive part of the code. We discuss several parallel implementations and propose an implementation which overlaps the communications by the computations to reach a better eeciency. We show t...

Implementation of parallel one-sided block Jacobi methods for the symmetric eigenvalue problem

A One-Sided Jacobi Algorithm for the Symmetric Eigenvalue Problem

A method which uses one-sided Jacobi to solve the symmetric eigenvalue problem in parallel is presented. We describe a parallel ring ordering for one-sided Jacobi computation. One distinctive feature of this ordering is that it can sort column norms in each sweep, which is very important to achieve fast convergence. Experimental results on both the Fujitsu AP1000 and the Fujitsu VPP500 are repo...

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms....

Improving the parallel performance of a domain decomposition preconditioning technique in the Jacobi-Davidson method for large scale eigenvalue problems

Most computational work in Jacobi-Davidson [9], an iterative method for large scale eigenvalue problems, is due to a so-called correction equation. In [5] a strategy for the approximate solution of the correction equation was proposed. This strategy is based on a domain decomposition preconditioning technique in order to reduce wall clock time and local memory requirements. This report discusse...