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Abstract: We describe two main classes of one-sided trigonometric and hyperbolicJacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitianmatrices. These types of algorithms exhibit significant advantages over manyother eigenvalue algorithms. If the matrices permit, both types of algorithmscompute the eigenvalues and eigenvectors with high relative accuracy.We present novel parallelization techniques for both trigonometric andhyperbolic classes of algorithms, as well as some new ideas on how pivoting ineach cycle of the algorithm can improve the speed of the parallel one-sidedalgorithms. These parallelization approaches are applicable to bothdistributed-memory and shared-memory machines.The numerical testing performed indicates that the hyperbolic algorithms maybe superior to the trigonometric ones, although, in theory, the latter seemmore natural.



Author: Sanja Singer, Sasa Singer, Vedran Novakovic, Aleksandar Uscumlic, Vedran Dunjko

Source: https://arxiv.org/







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