SIAM Journal on Scientific Computing · 1997 · 18 citations · 23 references
ComputingComputer ScienceHigh-performance ComputingParallel AlgorithmsParallel ComputingScientific ComputingMatrix ComputationNumerical Linear AlgebraParallel Algorithm DesignParallel ArchitecturesParallel ComputationParallel Numerical MethodsEigenvalue AlgorithmsEigenvalue ComputationEigenvalue ExtractionEigenvaluesMatrix MultiplicationParallel Eigenvalue ComputationParallel Matrix AlgorithmsParallel Matrix Computation
In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical considerations of the actual implementation. The numerical algorithm has been tested on thousands of matrices on both a Cray-2 and an IBM RS/6000 Model 580 workstation. The results of these tests are presented. Finally, issues concerning the parallel implementation of the algorithm are discussed. The algorithm's heavy reliance on matrix--matrix multiplication, coupled with the divide and conquer nature of this algorithm, should yield a highly parallelizable algorithm.
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Virginia Klema, Jack Dongarra, James R. Bunch et al. · Mathematics of Computation · 1980 · 648 citations