Solution to the Eigenproblem by a Norm Reducing Jacobi Type Method

  • P. J. Eberlein
  • J. Boothroyd
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


Let A be an n×n real matrix. A matrix T=T 1 T 2T i … (or T -1) is constructed as a product of a sequence of two dimensional transformations T i . From A′,= T -1 AT the eigenvalues may be read off and from T (or T -1) the right (or left) vectors. Each T i is of the form RS where R is a rotation and S a shear or complex rotation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Eberlein, P. J.: A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix. J. Soc. Indust. Appl. Math. 10, 74–88 (1962).MathSciNetCrossRefGoogle Scholar
  2. 2.
    Eberlein, P. J. Algorithms for the scaling of inner products with applications to linear least squares and the eigenproblem. Submitted to the SI AM J. Numer. Anal.Google Scholar
  3. 3.
    Eberlein, P. J.Solution to the complex eigenproblem by a norm reducing Jacobi type method. Numer. Math. 14, 232–245 (1970). Cf. 11/17.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • P. J. Eberlein
  • J. Boothroyd

There are no affiliations available

Personalised recommendations