# 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.