Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I

The dense nonsymmetric eigenproblem is one of the hardest linear algebra problems to solvee ectively on massivelyparallel machines. Rather than trying to design a black box" eigenroutine in the spirit of EISPACK or LAPACK, we propose building a toolbox for this problem. The tools are meant to be used in di erent combinations on di erent problems and architectures. In this paper, we will describe these tools which include basic block matrix computations, the matrix sign function, 2-dimensionalbisection, and spectral divide and conquer using the matrix sign function to nd selected eigenvalues. We also outline how we deal with ill-conditioning and potential instability. Numerical examplesare included. A future paper will discuss error analysis in detail and extensions to the generalized eigenproblem. Appears as Computer Science Division Tech Report UCB CSD-92-718, U. C. Berkeley, 1992 Research Report 92-09, Department of Mathematics, Univ. of Kentucky, 1992. Department of Mathemati...

• Type: Conference
• Year: 1993
• Where: PPSC
• Authors: Zhaojun Bai, James Demmel
• Keywords: Argonne National Laboratory, DARPA Grant, Matrix Sign Function, PPSC 1993, PPSC 2001