.TH "mic" 5rheolef "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
mic \- modified incomplete Cholesky factorization preconditionner (rheolef-7\&.2)
.SH "SYNOPSIS"
.PP
.PP
.nf
    solver pa = mic(a);
.fi
.PP
 
.SH "DESCRIPTION"
.PP
\fCmic\fP is a function that returns the modified incomplete Cholesky factorization preconditioner as a \fBsolver(4)\fP\&. The method is described in 
.PP
.nf
    C-J\&. Lin and J\&. J\&. More,
    Incomplete Cholesky factorizations with limited memory,
    SIAM J\&. Sci\&. Comput\&. 21(1), pp\&. 24-45, 1999

.fi
.PP
 It performs the following incomplete factorization: \fCS P A P^T S\fP that approximates \fCL L^T\fP where \fCL\fP is a lower triangular factor, \fCS\fP is a diagonal scaling matrix, and \fCP\fP is a fill-in reducing permutation as computed by the \fCAMDcol\fP ordering method\&.
.SH "OPTIONS"
.PP
This preconditioner supports an option related to the shifting strategy: let \fCB = S P A P^T S\fP be the scaled matrix on which the factorization is carried out, and \fCbeta\fP be the minimum value of the diagonal\&. If \fCbeta > 0\fP then, the factorization is directly performed on the matrix \fCB\fP\&. Otherwise, the factorization is performed on the shifted matrix \fCB + (shift+|beta|I\fP where \fCshift\fP is the provided option\&. The default value is \fCshift = 0\&.001\fP\&. If the factorization fails, then the shift is doubled until it succeed or a maximum of ten is reached\&. If it still fails, it is better to use another preconditioning technique\&. 
.PP
.nf
    Float shift = 1e-3;
    solver pa = mic (a,shift);

.fi
.PP
 
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file linalg/lib/mic\&.h 
.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH COPYRIGHT
Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr>
GPLv3+: GNU GPL version 3 or later  <http://gnu.org/licenses/gpl.html>.
This  is  free  software:  you  are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.