From 342e83fd8a4f49ce933ffc301e5c70bf349d3656 Mon Sep 17 00:00:00 2001 From: Timo Heister Date: Thu, 5 Feb 2015 09:30:34 -0500 Subject: [PATCH] update documentation --- include/deal.II/lac/sparse_mic.h | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/include/deal.II/lac/sparse_mic.h b/include/deal.II/lac/sparse_mic.h index aefa5923c7..50093282b7 100644 --- a/include/deal.II/lac/sparse_mic.h +++ b/include/deal.II/lac/sparse_mic.h @@ -26,17 +26,18 @@ DEAL_II_NAMESPACE_OPEN */ /** - * Modified incomplete Cholesky (MIC(0)) preconditioner. This class conforms - * to the state and usage specification in SparseLUDecomposition. + * Implementation of the Modified Incomplete Cholesky (MIC(0)) preconditioner + * for symmetric matrices. This class conforms to the state and usage + * specification in SparseLUDecomposition. * * *

The decomposition

* - * Let a sparse matrix $A$ be in the form $A = - L - U + D$, where $-L$ and - * $-U$ are strictly lower and upper triangular matrices. The MIC(0) - * decomposition of the matrix $A$ is defined by $B = (X-L)X^(-1)(X-U)$, where - * $X$ is a diagonal matrix, defined by the condition $\text{rowsum}(A) = - * \text{rowsum}(B)$. + * Let a symmetric, positive-definite, sparse matrix $A$ be in the form $A = D + * - L - L^T$, where $D$ is the diagonal part of $A$ and $-L$ is a strictly + * lower triangular matrix. The MIC(0) decomposition of the matrix $A$ is + * defined by $B = (X-L)X^{-1}(X-L^T)$, where $X$ is a diagonal matrix + * defined by the condition $\text{rowsum}(A) = \text{rowsum}(B)$. * * @author Stephen "Cheffo" Kolaroff, 2002, unified interface: Ralf Hartmann * 2003. -- 2.39.5