Xujun Zhao <[email protected]> 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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