Fastest way to compute spectral norm of a matrix?

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Michael 2013-6-11

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采纳的回答： Matt J

Hello

I can't find any mention of the spectral norm in the documentation. I want to calculate

max(|Ax|)/x for any vector x, given a matrix A.

There's a method via the eigenvalues of A'A but that sounds very memory intensive, I was wondering if anyone knows a faster in-built option.

Thanks

Mike

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Matt J 2013-6-11

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See the NORM command. It accepts matrix inputs.

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Matt J 2013-6-11

编辑：Matt J 2013-6-11

在 MATLAB Online 中打开

Yes. Try it:

    >> A=rand(5);
    >> max(sqrt(eig(A.'*A)))
    ans =
        2.2584
    >> norm(A)
    ans =
        2.2584

Matt J 2013-6-11

编辑：Matt J 2013-6-11

在 MATLAB Online 中打开

Hmmm. Looks like NORM is not as fast as the direct calculation,

    A=rand(1000);
    tic;
     n1=sqrt( max( eig(A.'*A) ) );
    toc; %Elapsed time is 0.150860 seconds.
    tic;
     n2=norm(A);
    toc; %Elapsed time is 0.319899 seconds.

However, I'm pretty sure it's because NORM uses SVD instead of EIG, which is probably more numerically stable.

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