What is the fastest way to compute the first eigenvector?

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.

Answer 1

[gonzalo Mier]

Read about eigs

[Shojiro SHIBAYAMA]

Hi,

It looks suitable for my task. Thank you for the quick reply.

[Meiling HU]

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]

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]

Really interesting! Thank you for contribute