Novel modifications of parallel Jacobi algorithms

Novel modifications of parallel Jacobi algorithms

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Article ID: iaor201113492
Volume: 59
Issue: 1
Start Page Number: 1
End Page Number: 27
Publication Date: Jan 2012
Journal: Numerical Algorithms
Authors: , , , ,
Keywords: numerical analysis
Abstract:

We describe two main classes of one‐sided trigonometric and hyperbolic Jacobi‐type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy. We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one‐sided algorithms. These parallelization approaches are applicable to both distributed‐memory and shared‐memory machines. The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural.

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