clarke@csri.toronto.edu (Jim Clarke) (04/06/89)
NUMERICAL ANALYSIS SEMINAR - Monday, April 10, 10 a.m. in Room GB 119
(GB = Galbraith Building, 35 St. George Street)
Elizabeth Jessup
Yale University
"Parallel Solution of the Symmetric Tridiagonal Eigenproblem"
Some methods for computing the eigendecomposition of a real symmetric
tridiagonal matrix exhibit both high accuracy and significant large-grained
parallelism appropriate for implementation on a local-memory MIMD
multiprocessor. These include Cuppen's divide and conquer strategy,
bisection with Sturm sequences coupled with inverse iteration, and the QR
method using computed eigenvalues as shifts. This presentation will
include a comparison of these methods with respect to accuracy, speed and
parallel efficiency on a hypercube multiprocessor. Factors influencing the
accuracy of eigenvectors computed by inverse iteration will be examined and
the use of a starting vector with random components analyzed statistically.
Adaptations of the eigensolvers to computing the singular value
decomposition (SVD) of a bidiagonal matrix will also be discussed. The
fastest, most parallel accurate method for both problems will be
identified.
--
Jim Clarke -- Dept. of Computer Science, Univ. of Toronto, Canada M5S 1A4
(416) 978-4058
clarke@csri.toronto.edu or clarke@csri.utoronto.ca
or ...!{uunet, pyramid, watmath, ubc-cs}!utai!utcsri!clarke