An Adaptive Multilevel Factorized Sparse Approximate Inverse Preconditioning

0473670 - ÚI 2018 RIV NL eng J - Journal Article
Kopal, Jiří - Rozložník, Miroslav - Tůma, Miroslav
An Adaptive Multilevel Factorized Sparse Approximate Inverse Preconditioning.
Advances in Engineering Software. Roč. 113, November (2017), s. 19-24. ISSN 0965-9978. E-ISSN 1873-5339
R&D Projects: GA ČR GA13-06684S
Grant - others:GA MŠk(CZ) LL1202
Institutional support: RVO:67985807
Keywords : approximate inverse * Gram–Schmidt orthogonalization * incomplete factorization * multilevel methods * preconditioned conjugate gradient method
OECD category: Applied mathematics
Impact factor: 3.198, year: 2017

This paper deals with adaptively preconditioned iterative methods for solving large and sparse systems of linear equations. In particular, the paper discusses preconditioning where adaptive dropping reflects the quality of preserving the relation UZ=I, where U and Z are the triangular factors of A and its inverse, respectively. The proposed strategy significantly extends and refines the previously developed approach, by using a specific multilevel framework. Numerical experiments with two levels demonstrate that the new preconditioning strategy is very promising. Namely, we show a surprising fact that in our approach the Schur complement is better to form in a more sophisticated way than by a standard sparse matrix-matrix multiplication.
Permanent Link: http://hdl.handle.net/11104/0270800