How to solve det(s^2M+sC(s)+K)=0 for s as fast as posible

Question

Rodrigo Moscoso Cires 2018-7-1

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https://ww2.mathworks.cn/matlabcentral/answers/408308-how-to-solve-det-s-2-m-s-c-s-k-0-for-s-as-fast-as-posible

回答： Sergey Kasyanov 2018-7-6

Hello, I want to solve the equation:

det(s^2*M+s*C(s)+K)=0

for s. In this equation M, C and K are big (at least 100x100), sparse matrices and C depends on s (it has the term (50/(s+50)) in it). Is there a faster way to solve this besides the following procedure?:

using the symbolic variable "s"
finding the determinant with the command det(s^2*M+s*C(s)+K)
solve the equation using the command solve(det(s^2*M+s*C(s)+K==0,s) and then
vpa(solve(det(s^2*M+s*C(s)+K)==0,s))

I tried to use polyeig(s^2*M+s*C(s)+K) as an alternative, but it just solves the equation for a constant C and not for C(s).

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Answer 1

Sergey Kasyanov 2018-7-6

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https://ww2.mathworks.cn/matlabcentral/answers/408308-how-to-solve-det-s-2-m-s-c-s-k-0-for-s-as-fast-as-posible#answer_327754

在 MATLAB Online 中打开

You can try to use that code from there:

    A=GaussElimination(s^2*M+s*C+K,'');
    [~,d]=numden(A(end,end));
    Solution=solve(d,s);

You must define C as symbolic matrix. Also I don't ensure that it will be work right, but you can rewrite GaussElimination() for your purpose (function GaussElimination() was wrote fast and for solving another narrow problem, but sometimes I use it for determinant calculation).