NAME
mic - modified incomplete Cholesky factorization preconditionner (rheolef-7.2)
SYNOPSIS
solver pa = mic(a);
DESCRIPTION
mic is a function that returns the modified incomplete Cholesky factorization preconditioner as a solver(4). The method is described in
C-J. Lin and J.
J. More,
Incomplete Cholesky factorizations with limited memory,
SIAM J. Sci. Comput. 21(1), pp. 24-45, 1999
It performs the following incomplete factorization: S P A P^T S that approximates L L^T where L is a lower triangular factor, S is a diagonal scaling matrix, and P is a fill-in reducing permutation as computed by the AMDcol ordering method.
OPTIONS
This preconditioner supports an option related to the shifting strategy: let B = S P A P^T S be the scaled matrix on which the factorization is carried out, and beta be the minimum value of the diagonal. If beta > 0 then, the factorization is directly performed on the matrix B. Otherwise, the factorization is performed on the shifted matrix B + (shift+|beta|I where shift is the provided option. The default value is shift = 0.001. 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.
Float shift =
1e-3;
solver pa = mic (a,shift);
IMPLEMENTATION
This documentation has been generated from file linalg/lib/mic.h
AUTHOR
Pierre Saramito <Pierre.Saramito [AT] imag.fr>
COPYRIGHT
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito [AT] 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.