[petsc-users] complexity of solvers

[Alexander Grayver]

Thanks for references, Jed!

Yes, they have 2D problem.

Regards,
Alexander

On 20.04.2011 17:45, Jed Brown wrote:
> On Wed, Apr 20, 2011 at 17:31, Alexander Grayver 
> <agrayver at gfz-potsdam.de <mailto:agrayver at gfz-potsdam.de>> wrote:
>
>     I came across with paper in one of the referenced journal where
>     authors claim that LU decomposition has complexity of
>     O(n^1.5) and one solution using factorized matrix can be
>     calculated in O(n*logn).
>
>
> These are the bounds for 2D problems with optimal ordering. For 3D, 
> the bounds are O(n^2) time and O(n^{4/3}) space.
>
> Alan George, Joseph Liu, Computer Solution of Large Sparse Positive 
> Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
>
> S.C. Eisenstat, M.H. Schultz, A.H. Sherman, Applications of an element 
> model for Gaussian elimination, in: Sparse Matrix Computations (Proc. 
> Symp., Argonne Nat. Lab., Lemont, Ill., 1975), Academic Press, New 
> York, 1976, pp. 85–96.
>

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