Accelerating eigenvector and pseudospectra computation using blocked multi-shift triangular solves Article Swipe
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Tim Moon
,
Jack Poulson
·
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1607.01477
· OA: W2468739001
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1607.01477
· OA: W2468739001
Multi-shift triangular solves are basic linear algebra calculations with applications in eigenvector and pseudospectra computation. We propose blocked algorithms that efficiently exploit Level 3 BLAS to perform multi-shift triangular solves and safe multi-shift triangular solves. Numerical experiments indicate that computing triangular eigenvectors with a safe multi-shift triangular solve achieves speedups by a factor of 60 relative to LAPACK. This algorithm accelerates the calculation of general eigenvectors threefold. When using multi-shift triangular solves to compute pseudospectra, we report ninefold speedups relative to EigTool.
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