Dominant eigenvalue using the inverse power method

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Enzo Carzola 2014-5-3

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https://ww2.mathworks.cn/matlabcentral/answers/128142-dominant-eigenvalue-using-the-inverse-power-method

评论： Geoff Hayes 2014-5-3

I wrote the code for the inverse power method and the latter is giving me the least dominant eigenvalue. Here is my code

function [v,lamda] = IPM(B,tol)

tic;

A=inv(B);

n=size(A,1);

v=rand(n,1);

v=v/norm(v);

res=1;

while (res > tol)

W= A*v;

lamda=max(abs(W));

v= W/lamda;

res=norm(A*v-lamda*v);

toc

end

I want to invert it to get the dominant eigenvalue. Please help.

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Geoff Hayes 2014-5-3

It is my understanding that the Power Method returns the dominant eigenvalue, and that the Inverse Power Method can be used to find the smallest (least dominant) eigenvalue OR it can be used to approximate an eigenvalue close to some number (which implies the least dominant eigenvalue if the chosen number is zero…which is the case in the above code).

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