TY  - JOUR
T1  - Factorized approximate inverses with adaptive dropping
A1  - Kopal, Jiří
A1  - Rozložník, Miroslav
A1  - Tůma, Miroslav
JA  - SIAM Journal on Scientific Computing
Y1  - 2016
VL  - 38
IS  - 3
SP  - A1807–A1820
M2  - doi: 10.1137/15M1030315
KW  - Approximate inverses
KW  - Gram–Schmidt orthogonalization
KW  - incomplete factorization
KW  - preconditioned iterative methods
N2  - This paper presents a new approach to construct factorized approximate inverses for a symmetric and positive definite matrix A. The proposed strategy is based on adaptive dropping that reflects the quality of preserving the relation UZ = I between the direct factor U and the inverse factor Z satisfying A = UT U and A−1 = ZZT . An important part of the approach is column pivoting used to minimize the growth of the condition number of leading principal submatrices of U that occurs explicitly in the dropping criterion. Numerical experiments demonstrate that the resulting approximate inverse factorization is robust as a preconditioner for solving large and sparse systems of linear equations.
M1  - Preprint project = NCMM
M1  - Preprint year = 2016
M1  - Preprint number = 02
M1  - Preprint ID = NCMM/2016/02
ER  -