Getting inaccurate eigenvalue with eig command. Please suggest me some other command or small series of steps to find accurate eigen value for Generalized Eigenvalue Problem.

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% For Generalized Eigenvalue problem Ax = λBx, where A and B are of order 12*12.
A =[ -11.0913 0 0 0 0 0 0 0 0 0 0 0;
0 -25.8957 0 0 0 0 0 0 0 0 0 0;
0 0 -50.5698 0 0 0 0 0 0 0 0 0;
0 0 0 -85.1134 0 0 0 0 0 0 0 0;
0 0 0 0 -129.5266 0 0 0 0 0 0 0;
0 0 0 0 0 -183.8094 0 0 0 0 0 0;
0.5000 0 0 0 0 0 -11.0913 0 0 0 0 0;
0 0.5000 0 0 0 0 0 -25.8957 0 0 0 0;
0 0 0.5000 0 0 0 0 0 -50.5698 0 0 0;
0 0 0 0.5000 0 0 0 0 0 -85.1134 0 0;
0 0 0 0 0.5000 0 0 0 0 0 -129.5266 0;
0 0 0 0 0 0.5000 0 0 0 0 0 -183.8094]
B = [ 0 0 0 0 0 0 -1.5391 -1.6634 0 -0.1331 0 -0.0367;
0 0 0 0 0 0 -1.6634 -1.5391 -1.7965 0 -0.1697 0;
0 0 0 0 0 0 0 -1.7965 -1.5391 -1.8332 0 -0.1848;
0 0 0 0 0 0 -0.1331 0 -1.8332 -1.5391 -1.8483 0;
0 0 0 0 0 0 0 -0.1697 0 -1.8483 -1.5391 -1.8559;
0 0 0 0 0 0 -0.0367 0 -0.1848 0 -1.8559 -1.5391;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0]
e1=eig(A,B);
min(e1(e1>-inf)) % extracting minimum of eig(A,B) which is greater than -inf.
= -3.8410e+04 % But exact value in the paper is 132.020.
% Please mention some other command or way or small series of steps to find the the required eigen value as 132.020.

Accepted Answer

Alan Stevens
Alan Stevens on 30 Nov 2022
Like this:
A =[ -11.0913 0 0 0 0 0 0 0 0 0 0 0;
0 -25.8957 0 0 0 0 0 0 0 0 0 0;
0 0 -50.5698 0 0 0 0 0 0 0 0 0;
0 0 0 -85.1134 0 0 0 0 0 0 0 0;
0 0 0 0 -129.5266 0 0 0 0 0 0 0;
0 0 0 0 0 -183.8094 0 0 0 0 0 0;
0.5000 0 0 0 0 0 -11.0913 0 0 0 0 0;
0 0.5000 0 0 0 0 0 -25.8957 0 0 0 0;
0 0 0.5000 0 0 0 0 0 -50.5698 0 0 0;
0 0 0 0.5000 0 0 0 0 0 -85.1134 0 0;
0 0 0 0 0.5000 0 0 0 0 0 -129.5266 0;
0 0 0 0 0 0.5000 0 0 0 0 0 -183.8094];
B = [ 0 0 0 0 0 0 -1.5391 -1.6634 0 -0.1331 0 -0.0367;
0 0 0 0 0 0 -1.6634 -1.5391 -1.7965 0 -0.1697 0;
0 0 0 0 0 0 0 -1.7965 -1.5391 -1.8332 0 -0.1848;
0 0 0 0 0 0 -0.1331 0 -1.8332 -1.5391 -1.8483 0;
0 0 0 0 0 0 0 -0.1697 0 -1.8483 -1.5391 -1.8559;
0 0 0 0 0 0 -0.0367 0 -0.1848 0 -1.8559 -1.5391;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0];
e1=eig(A,B);
disp(min(abs(e1)))
132.0221

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