Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices

Details Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices

2010-08-24

arxiv.org/abs/1008.4166v1

Computer Science

Numerical Analysis

Submitted for publication

Scientific paper

10.1016/j.amc.2011.11.067

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.

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