rosser

Purpose

A classic symmetric eigenvalue test problem.

Synopsis

A = rosser

Description

This matrix was a challenge for many matrix eigenvalue algorithms. But the Francis QR algorithm, as perfected by Wilkinson and implemented in EISPACK and MATLAB, has no trouble with it. The matrix is 8-by-8 with integer elements. It has

  • A double eigenvalue
  • Three nearly equal eigenvalues
  • Dominant eigenvalues of opposite sign
  • A zero eigenvalue
  • A small, nonzero eigenvalue
    The Rosser matrix is:

        611   196  -192   407    -8   -52   -49    29
    196   899   113  -192   -71   -43    -8   -44
   -192   113   899   196    61    49     8    52
    407  -192   196   611     8    44    59   -23
     -8   -71    61     8   411  -599   208   208
    -52   -43    49    44  -599   411   208   208
    -49    -8     8    59   208   208    99  -911
     29   -44    52   -23   208   208  -911    99
    Its exact eigenvalues are

        10*sqrt(10405)
          
    1020
          
    510 + 100*sqrt(26)
          
    1000
          
    1000
          
    510 - 100*sqrt(26)
          
    0
          
    -10*sqrt(10405)

    See Also

    eig, gallery, wilkinson

    (c) Copyright 1994 by The MathWorks, Inc.