Re: Eigenvector extraction


Fijoy George wrote:
> Hi all,
>
> I am trying to extract the eigenvectors corresponding to the k smallest
> magnitude eigenvalues of a large and sparse matrix (~ 50000x50000) for some
> k. Currently I am using the eigs() function in MATLAB which in turn calls
> ARPACK routines. However, since memory can hold only a limited number of
> eigenvectors simultaneously, I am not able to increase k beyond a certain
> value.
>
> Anyone encountereed this problem before? Is there a solution to this
> problem?
>
> Specifically, I am thinking if something like the following is possible.
> First I extract the first k/2 eigenvectors and save them to the disk, and
> then, using some mathematical/algorithmic techniques, extract the rest of
> the eigenvectors. Does anyone know if this can be done?
>
> -Fijoy
Here as an idea that probably won't work. Form the matrix made up of
the largest eignvalues and there corresponding eignvectors. V Lambada
V' or something like that. Then subtract it from the matrix in
question and then try to find the remaining eigenvectors. Another idea
that probably won't work is to invert the matrix and then find the
eign vectors. The eigenvectors should remain unchanged but the
eignvalues should be inverted I think.

.

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