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@imag.fr>

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.