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.

% 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.

[David Goodmanson]

Hi arpan,

of the noninfinite eigenvalues the maximum one is 132.02

Answer 1

[Alan Stevens]

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

[arpan garg]

Thank you very much sir. It has served whatever was needed. Thank you very much.