---
name: "mic"
section: "5rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/mic/5rheolef"
---

# mic(5rheolef)

modified incomplete Cholesky factorization preconditionner (rheolef-7.2)

## 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.