Numerische Mathematik

, Volume 76, Issue 3, pp 279–308

An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems

  • Zhaojun Bai
  • James Demmel
  • Ming Gu

DOI: 10.1007/s002110050264

Cite this article as:
Bai, Z., Demmel, J. & Gu, M. Numer. Math. (1997) 76: 279. doi:10.1007/s002110050264


We discuss an inverse-free, highly parallel, spectral divide and conquer algorithm. It can compute either an invariant subspace of a nonsymmetric matrix \(A\), or a pair of left and right deflating subspaces of a regular matrix pencil \(A - \lambda B\). This algorithm is based on earlier ones of Bulgakov, Godunov and Malyshev, but improves on them in several ways. This algorithm only uses easily parallelizable linear algebra building blocks: matrix multiplication and QR decomposition, but not matrix inversion. Similar parallel algorithms for the nonsymmetric eigenproblem use the matrix sign function, which requires matrix inversion and is faster but can be less stable than the new algorithm.

Mathematics Subject Classification (1991):65F15 

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Zhaojun Bai
    • 1
  • James Demmel
    • 2
  • Ming Gu
    • 3
  1. 1.Department of Mathematics, University of Kentucky, Lexington, KY 40506, USAUS
  2. 2.Computer Science Division and Mathematics Department, University of California, Berkeley, CA 94720, USAUS
  3. 3.Department of Mathematics and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USAUS

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