Accelerating eigenvector and pseudospectra computation using blocked multishift triangular solves
Abstract
Multishift 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 multishift triangular solves and safe multishift triangular solves. Numerical experiments indicate that computing triangular eigenvectors with a safe multishift triangular solve achieves speedups by a factor of 60 relative to LAPACK. This algorithm accelerates the calculation of general eigenvectors threefold. When using multishift triangular solves to compute pseudospectra, we report ninefold speedups relative to EigTool.
 Publication:

arXiv eprints
 Pub Date:
 July 2016
 arXiv:
 arXiv:1607.01477
 Bibcode:
 2016arXiv160701477M
 Keywords:

 Computer Science  Mathematical Software;
 Computer Science  Numerical Analysis;
 Mathematics  Numerical Analysis
 EPrint:
 20 pages, 6 figures