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

Subject: Re: [ublas] Modified incomplete cholesky factorization (no fill ins)
From: Paul C. Leopardi (paul.leopardi_at_[hidden])
Date: 2009-03-27 07:54:40

On Wed, 25 Mar 2009, AQMS wrote:
> 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.

Hi Aznul,
I am not an expert, but I took a quick look at the literature and the 
following paper may interest you:

Jones, M. T. and Plassmann, P. E. 1995. An improved incomplete Cholesky 
factorization. ACM Trans. Math. Softw. 21, 1 (Mar. 1995), 5-17. 
DOI= http://doi.acm.org/10.1145/200979.200981

It describes two alternatives to MIC(0) that may be more suitable to your 
needs, and includes pseudocode.
Best, Paul