rosser (MATLAB C++ Math Library)

Classic symmetric eigenvalue test matrix (Rosser)

C++ Prototype

mwArray rosser();

C++ Syntax

#include "matlab.hpp"

mwArray c;                  // Input argument(s)
mwArray A;                  // Return value

A = rosser();

MATLAB Syntax

[A,B,C,...] = gallery('tmfun',P1,P2,...)
gallery(3)             a badly conditioned 3-by-3 matrix
gallery(5)             an interesting eigenvalue problem

Description

A = rosser();

returns the Rosser matrix. 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