# Inverse Free Parallel Spectral Divide and Conquer Algorithms for Nonsymmetric Eigenproblems

### Zhaojun Bai, James W. Demmel and Ming Gu

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-94-793

February 1994

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/CSD-94-793.pdf

We discuss two inverse free, highly parallel, spectral divide and conquer algorithms: one for computing an invariant subspace of a nonsymmetric matrix and another one for computing left and right deflating subspaces of a regular matrix pencil
*A* - lambda
*B*. These two closely related algorithms are based on earlier ones of Bulgakov, Godunov and Malyshev, but improve on them in several ways. These algorithms only use easily parallelizable linear algebra building blocks: matrix multiplication and QR decomposition. The existing parallel algorithms for the nonsymmetric eigenproblem use the matrix sign function, which is faster but can be less stable than the new algorithm.

BibTeX citation:

@techreport{Bai:CSD-94-793, Author = {Bai, Zhaojun and Demmel, James W. and Gu, Ming}, Title = {Inverse Free Parallel Spectral Divide and Conquer Algorithms for Nonsymmetric Eigenproblems}, Institution = {EECS Department, University of California, Berkeley}, Year = {1994}, Month = {Feb}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5383.html}, Number = {UCB/CSD-94-793}, Abstract = {We discuss two inverse free, highly parallel, spectral divide and conquer algorithms: one for computing an invariant subspace of a nonsymmetric matrix and another one for computing left and right deflating subspaces of a regular matrix pencil <i>A</i> - lambda <i>B</i>. These two closely related algorithms are based on earlier ones of Bulgakov, Godunov and Malyshev, but improve on them in several ways. These algorithms only use easily parallelizable linear algebra building blocks: matrix multiplication and QR decomposition. The existing parallel algorithms for the nonsymmetric eigenproblem use the matrix sign function, which is faster but can be less stable than the new algorithm.} }

EndNote citation:

%0 Report %A Bai, Zhaojun %A Demmel, James W. %A Gu, Ming %T Inverse Free Parallel Spectral Divide and Conquer Algorithms for Nonsymmetric Eigenproblems %I EECS Department, University of California, Berkeley %D 1994 %@ UCB/CSD-94-793 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5383.html %F Bai:CSD-94-793