19.num/JWD.ZB.robinson
.ls 2
.na
.LP
Parallel Algorithms for the Nonsymmetric Eigenproblem

Howard Robinson

(Professors J. W. Demmel and Z. Bai*)

(ARPA) DAAL03-91-C-0047 and (NSF) ASC-90-05933

The dense nonsymmetric eigenproblem is one of the hardest linear
algebra problems to solve effectively on massively parallel machines.
Rather than trying to design a "black box" eigenroutine in the spirit
of EISPACK or LAPACK, we are building a toolbox for this problem. The
tools are meant to be used in different combinations on different
problems and architectures. These tools include basic block matrix
computations, the matrix sign function, two-dimensional bisection, and
spectral divide and conquer using the matrix sign function to find
selected eigenvalues. We have a partial error analysis, and know how
to extend the methods to the generalized nonsymmetric eigenproblem. We
have attained excellent speedups on the CM-5, Intel Gamma, and Intel
Delta, whereas the standard serial algorithm offers only fine-grain
parallelism that is difficult to exploit.

* University of Kentucky