[SciPy-User] What is the complexity of scipy.sparse.linalg.eigsh

David Cournapeau cournape@gmail....
Tue Sep 13 22:41:00 CDT 2011

On Tue, Sep 13, 2011 at 10:48 PM, rechardchen <rechardchen@gmail.com> wrote:
> Hi, all
>       Recently I am using scipy.sparse.linalg.eigsh to compute K smallest
> eigenvalues(and their eigenvectors), but I have no idea how fast the
> function  runs. I know it uses ARPACK's implicitly restarted Lanczos Method,
> but I found no such information on ARPACK's official site.

It depends on your input (sparsity of the matrix). Assuming a square,
dense matrix of nrows, the cost is O(n^2 * k), keeping in mind the
constant can be pretty high. It is also data dependent, as the method
is iterative (there are no algebraic solutions to eigenvalues problems
in general).



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