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### A Sample Diagonalization Problem

We attempt to simultaneously diagonalize two noisy (random noise) versions of diag(1:10) and diag(1:10)^2. Our initial point is a small random perturbation of the identity.

>> !cp examples/simdiag/*.m .
>> randn('state',0);
>> [A,B] = noisy;
>> parameters(A,B);
>> Y0 = guess;
>> [fn,Yn] = sg_min(Y0,'frcg','euclidean');
0       2.887592e+03    9.671138e+02        30940
1       1.419011e+03    2.411349e+02       343392
2       6.199732e+02    7.601495e+01       718792
3       3.051636e+02    3.300591e+01      1106535
4       2.538995e+02    2.078422e+01      1518380
5       1.440247e+02    1.258174e+01      1923273
6       1.189063e+02    9.500450e+00      2332153
7       9.279907e+01    7.309071e+00      2743897
8       8.483878e+01    6.093323e+00      3161294
9       7.763100e+01    4.117233e+00      3609412
10      7.448803e+01    3.220241e+00      4026633
11      6.404668e+01    2.328540e+00      4439092
.......(many iterations later).......
169     2.196881e-06    4.010660e-07     67843218
170     2.309773e-06    4.010660e-07     68212219
171     2.435095e-06    4.010660e-07     68558476
172     1.763263e-06    4.010660e-07     68946596
173     2.081518e-06    4.010660e-07     69314166
174     1.251419e-06    4.010660e-07     69639992
175     1.474565e-06    4.010660e-07     70028565
176     8.949991e-07    4.010660e-07     70353929
177     8.506853e-07    4.010660e-07     70742988
178     7.154996e-07    4.010660e-07     71068090
179     8.003997e-07    4.010660e-07     71395085
180     3.164977e-07    4.010660e-07     71721113
181     3.701357e-07    4.010660e-07     72030590


Figure 9.6 shows the convergence curve for this run.

Susan Blackford 2000-11-20