What is the fastest way to compute the first eigenvector?

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Shojiro SHIBAYAMA 2019-6-10

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评论： gonzalo Mier 2020-4-3

I'd like to know a way to compute the first eigenvector (the eigenvector with the largest eigenvalue) of a matrix A. Now I am using eig function.

[V, D] = eig(A);

However, this computes all eigenvectors of A, resulting in slow computation.

Does anyone know if there is a fastest way to compute the eigenvector? Thank you in advance.

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gonzalo Mier 2019-6-10

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Read about eigs

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Shojiro SHIBAYAMA 2020-2-10

编辑：Shojiro SHIBAYAMA 2020-2-10

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Wow thank you for the fruitful reply. I also have saw the results:

>> A=randn(100, 10);
>> AtA = A'*A;
>> rank(AtA)
    10
>> tic;for i = 1:1000; eig(AtA);end; toc;
    Elapsed time is 0.000973 seconds.
>> tic;for i = 1:1000; eigs(AtA);end; toc;
    Elapsed time is 0.247325 seconds.    

I am going to replace eigs with eig.

gonzalo Mier 2020-4-3

Really interesting! Thank you for contribute

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