[ublas] Modified incomplete cholesky factorization (no fill ins)

Subject: [ublas] Modified incomplete cholesky factorization (no fill ins)
From: AQMS (azqalidd_at_[hidden])
Date: 2009-03-25 04:30:52

Hi all,

At the moment, I am trying to solve a very large sparse linear system using preconditioned conjugate gradient method.
I've tried the incomplete cholesky as a preconditioner, although this was successful in reducing the number of iterations to converge, it is possible to reduce the iterations even more using the modified incomplete cholesky factorization method (MIC).

My matrix is both symmetric and positive definite.
The reason that I wanted to use the MIC(0) (note that the 0 stands for no fill ins) is because I wish to maintain the original structure of the matrix.

I have read a lot of reference material, however, none gave explicit detail on how to perform this method of factorization, instead of simply giving a clue of maintaining/ keeping the fill values in the diagonal elements by subtracting the fill value from the diagonal element.

I've tried this, but I havent managed to get the desired result.
I know it might not be the correct place to ask this question, but I would appreciate if someone might point me in the right direction on the sequence of steps to perform this method of factorization.

Regards,
Aznul