# 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