Factorized Approximate Inverses With Adaptive Dropping

0456004 - ÚI 2017 RIV US eng J - Článek v odborném periodiku
Kopal, Jiří - Rozložník, Miroslav - Tůma, Miroslav
Factorized Approximate Inverses With Adaptive Dropping.
SIAM Journal on Scientific Computing. Roč. 38, č. 3 (2016), A1807-A1820. ISSN 1064-8275. E-ISSN 1095-7197
Grant CEP: GA ČR GA13-06684S
Grant ostatní: GA MŠk(CZ) LL1202
Institucionální podpora: RVO:67985807
Klíčová slova: approximate inverses * incomplete factorization * Gram–Schmidt orthogonalization * preconditioned iterative methods
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 2.195, rok: 2016

This paper presents a new approach to constructing 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 $A = U^TU$ and $A^{-1}=ZZ^T$. 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.
Trvalý link: http://hdl.handle.net/11104/0256585