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What is the fastest way to compute the first eigenvector?

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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
gonzalo Mier 10 Jun 2019
Read about eigs

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Meiling HU
Meiling HU 9 Feb 2020
It seems that eigs takes longer time to compute than eig. For 100 iterations of 25*25 matrix, eigs takes 1 sec while eig only takes 0.06.
Shojiro SHIBAYAMA
Shojiro SHIBAYAMA 10 Feb 2020
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
gonzalo Mier 3 Apr 2020
Really interesting! Thank you for contribute

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