NAME

       mic - modified incomplete Cholesky factorization preconditionner (rheolef-7.1)

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.

Version 7.1                                      Sun Oct 31 2021                                   mic(5rheolef)