Factorized Sparse Approximate Inverse Preconditionings I. Theory
Factorized Sparse Approximate Inverse Preconditionings I. Theory
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DOI：
10.1137/0614004
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
L. Kolotilina;A. Yeremin
中科院分区：
文献类型：
--
作者：
L. Kolotilina;A. Yeremin
本文考虑了分解的稀疏近似逆预处理的构建和特性，非常适合在现代平行计算机上实现。在对称情况下，此类预处具有$ a \ to g_l ag_l^t $的形式，其中$ g_l $是基于最小化frobenius form $ \ |的稀疏近似值。 i -g_l l_a \ | _f $ to下三角形cholesky因子$ l_a $ a的倒数，这并不明确地知道。这些预处理保留原始矩阵的对称性和/或正定性，在M-，H-或阻断H-矩阵的情况下，会导致收敛分裂。
This paper considers construction and properties of factorized sparse approximate inverse preconditionings well suited for implementation on modern parallel computers. In the symmetric case such preconditionings have the form $A \to G_L AG_L^T $, where $G_L $ is a sparse approximation based on minimizing the Frobenius form $\| I - G_L L_A \|_F $ to the inverse of the lower triangular Cholesky factor $L_A $ of A, which is not assumed to be known explicitly. These preconditionings preserve symmetry and/or positive definiteness of the original matrix and, in the case of M-, H-, or block H-matrices, lead to convergent splittings.