Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I

Zhaojun Bai and James W. Demmel

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-92-718
February 1993

http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-718.pdf

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 propose building a toolbox for this problem. The tools are meant to be used in different combinations on different problems and architectures. In this paper, we will describe these tools which include basic block matrix computations, the matrix sign function, 2-dimensional bisection, and spectral divide and conquer using the matrix sign function to find selected eigenvalues. We also outline how we deal with ill-conditioning and potential instability. Numerical examples are included. A future paper will discuss error analysis in detail and extensions to the generalized eigenproblem.


BibTeX citation:

@techreport{Bai:CSD-92-718,
    Author = {Bai, Zhaojun and Demmel, James W.},
    Title = {Design of a Parallel Nonsymmetric Eigenroutine Toolbox,  Part I},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1993},
    Month = {Feb},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/6014.html},
    Number = {UCB/CSD-92-718},
    Abstract = {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 propose building a toolbox for this problem. The tools are meant to be used in different combinations on different problems and architectures. In this paper, we will describe these tools which include basic block matrix computations, the matrix sign function, 2-dimensional bisection, and spectral divide and conquer using the matrix sign function to find selected eigenvalues. We also outline how we deal with ill-conditioning and potential instability. Numerical examples are included. A future paper will discuss error analysis in detail and extensions to the generalized eigenproblem.}
}

EndNote citation:

%0 Report
%A Bai, Zhaojun
%A Demmel, James W.
%T Design of a Parallel Nonsymmetric Eigenroutine Toolbox,  Part I
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/CSD-92-718
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/6014.html
%F Bai:CSD-92-718