Eig takes too long

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bil
bil on 16 Jun 2022
Answered: Walter Roberson on 16 Jun 2022
Hi All,
I am currently trying to find the eigenvectors for this 5x5 matrix but Matlab seems to be taking incredibly long to do so:
syms a b c d e f g h k l
p2 = [0 1/(a)^3 1/(b)^3 1/(c)^3 1/(d)^3;
1/(a)^3 0 1/(e)^3 1/(f)^3 1/(g)^3;
1/(b)^3 1/(e)^3 0 1/(h)^3 1/(k)^3;
1/(c)^3 1/(f)^3 1/(h)^3 0 1/(l)^3;
1/(d)^3 1/(g)^3 1/(k)^3 1/(l)^3 0];
[V,D]=eig(p2);
We can assume here that none of the variables are 0.
Does anyone have any suggestions or advice that can help speed up this calculation if that is even possible?
(I need to keep the matrix in symbolic form because I will need to manipulate the variable directly in a later calculation).
Thank you!

Answers (2)

Matt J
Matt J on 16 Jun 2022
Edited: Matt J on 16 Jun 2022
Does anyone have any suggestions or advice that can help speed up this calculation if that is even possible?
I don't think the calculation itself is possible. A symbolic solution would mean finding the roots of a 5th order characteristic polynomial, which is theoretically known to have no analytical solutions,
I need to keep the matrix in symbolic form because I will need to manipulate the variable directly in a later calculation
That doesn't explain why you need sym. Please clarify.
  2 Comments
Matt J
Matt J on 16 Jun 2022
There are numerical ODE functions in Matlab,
Is there a reason one of them wouldn't apply?

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Walter Roberson
Walter Roberson on 16 Jun 2022
syms M [5 5];
M = M - diag(diag(M));
[V, D] = eig(M);
When that eventually finishes (which will take a while), you can subs() actual expressions in place of symvars(M). Expect the subs() to take a while too.
Abandon hope of simplify() the results. And do not be surprised if it involves root() of a polynomial of degree 5.
...Prepare for the possibility that the results will be too large to be of any practical use.

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