Geodesic
Preconditioned recycling Krylov subspace methods for self-adjoint problems
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 522-547
A recycling Krylov subspace method for the solution of a sequence of self-adjoint linear systems is proposed. Such problems appear, for example, in the Newton process for solving nonlinear equations. Ritz vectors are automatically extracted from one MINRES run and then used for self-adjoint deflation in the next. The method is designed to work with arbitrary inner products and arbitrary self-adjoint positive-definite preconditioners whose inverse can be computed with high accuracy. Numerical experiments with nonlinear Schrödinger equations indicate a substantial decrease in computation time when recycling is used.
Classification : 65F10, 65F08, 35Q55, 35Q56
Keywords: Krylov subspace methods, MINRES, deflation, Ritz vector recycling, nonlinear Schrödinger equations, Ginzburg, Landau equations 
@article{ETNA_2015__44__a5,
     author = {Gaul,  Andr\'e and Schl\"omer,  Nico},
     title = {Preconditioned recycling {Krylov} subspace methods for self-adjoint problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {522--547},
     year = {2015},
     volume = {44},
     zbl = {1327.65059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a5/}
}
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AU  - Gaul,  André
AU  - Schlömer,  Nico
TI  - Preconditioned recycling Krylov subspace methods for self-adjoint problems
JO  - Electronic transactions on numerical analysis
PY  - 2015
SP  - 522
EP  - 547
VL  - 44
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__44__a5/
LA  - en
ID  - ETNA_2015__44__a5
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%A Gaul,  André
%A Schlömer,  Nico
%T Preconditioned recycling Krylov subspace methods for self-adjoint problems
%J Electronic transactions on numerical analysis
%D 2015
%P 522-547
%V 44
%U http://geodesic.mathdoc.fr/item/ETNA_2015__44__a5/
%G en
%F ETNA_2015__44__a5
Gaul,  André; Schlömer,  Nico. Preconditioned recycling Krylov subspace methods for self-adjoint problems. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 522-547. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a5/