[petsc-users] estimation of max and min eigenvalues in SLEPc

[Jed Brown]

Xujun Zhao <xzhao99 at gmail.com> writes:

> I need to evaluate the max and min eigenvalues of a matrix 

You need the min and max eigenvalues of the preconditioner operator.
But note that Chebyshev is not usually used as a stand-alone solver, but
rather as a smoother for multigrid or occasionally as a polynomial
preconditioner to control storage requirements or orthogonalization
issues.  One exception is if your problem is fairly well-conditioned
with an evenly spaced spectrum.

In general, estimating the largest eigenvalue is relatively inexpensive,
but computing the smallest to even moderate accuracy is as expensive as
solving the linear system.

https://scicomp.stackexchange.com/questions/34/how-can-i-estimate-the-condition-number-of-a-large-sparse-matrix-using-petsc

> when I make the Chebyshev polynomial approximation. Are there
> efficient ways to do this?  Thank you very much.
>
> Xujun
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