Advertisement

Diagonalization of Hermitian Matrices; Maximization of Speed and Accuracy

  • R. A. Faulkner
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

In this paper I describe an algorithm for finding all of the eigenvalues and eigenvectors of an Hermitian matrix (either complex or real, symmetric). The algorithm is a combination of Householder reduction to tri-diagonal form and a modified QR method for obtaining both eigenvalues and eigenvectors of the reduced matrix. The central new practical technique communicated here lies in the modification of the QR method when generating eigenvectors along with the eigenvalues.

Keywords

Hermitian Matrix Hermitian Matrice Eigenvector Matrix Inverse Iteration Householder Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    J. H. Wilkinson, The Algebraic Eigenvalue Problem. Clarendon Press, Oxford (1965).Google Scholar
  2. (2).
    J. G. F. Francis, Computer J. 4, 265 and 332 (1961).CrossRefGoogle Scholar
  3. (3).
    HECEVV is part of a larger package available from the GESHUA Library: HEMP — High Efficiency Matrix Package, GES1030, GE-600 Series Users’ Library. HEMP is written in assembly language for General Electric 600-Series computers.Google Scholar
  4. (4).
    W. Kahan and J. Varah, Computer Science Department Technical Report No. CS43, Stanford University (1966).Google Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • R. A. Faulkner
    • 1
  1. 1.Bell Telephone Laboratories, IncorporatedMurray HillUSA

Personalised recommendations