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.