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Robust additive block triangular preconditioners for block two-by-two linear systems.
- Source :
-
Numerical Algorithms . Oct2019, Vol. 82 Issue 2, p503-537. 35p. - Publication Year :
- 2019
-
Abstract
- In this paper, a class of additive block triangular preconditioners are constructed for solving block two-by-two linear systems with symmetric positive (semi-)definite sub-matrices. Convergence analysis of the related splitting iteration method shows that it is almost unconditionally convergent and behaves problem independent with a convergence rate less than 0.5 under a practical parameter choice. Optimization of the preconditioned matrices, which have real and tight eigenvalue distributions, shows that it can result in an upper bound less than 2 for the condition number of the preconditioned matrices. Moreover, we also give a special consideration about the feasibility of the proposed preconditioner for solving more general problems with indefinite sub-matrices. Numerical experiments based on examples arising from complex symmetric linear systems and PDE-constrained optimization problems are presented to show the robustness and effectiveness of the proposed preconditioners compared with some other existing preconditioners. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 82
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 138631901
- Full Text :
- https://doi.org/10.1007/s11075-018-0611-2