3,634 research outputs found
From low-rank approximation to an efficient rational Krylov subspace method for the Lyapunov equation
We propose a new method for the approximate solution of the Lyapunov equation
with rank- right-hand side, which is based on extended rational Krylov
subspace approximation with adaptively computed shifts. The shift selection is
obtained from the connection between the Lyapunov equation, solution of systems
of linear ODEs and alternating least squares method for low-rank approximation.
The numerical experiments confirm the effectiveness of our approach.Comment: 17 pages, 1 figure
Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator
In lattice QCD computations a substantial amount of work is spent in solving
discretized versions of the Dirac equation. Conventional Krylov solvers show
critical slowing down for large system sizes and physically interesting
parameter regions. We present a domain decomposition adaptive algebraic
multigrid method used as a precondtioner to solve the "clover improved" Wilson
discretization of the Dirac equation. This approach combines and improves two
approaches, namely domain decomposition and adaptive algebraic multigrid, that
have been used seperately in lattice QCD before. We show in extensive numerical
test conducted with a parallel production code implementation that considerable
speed-up over conventional Krylov subspace methods, domain decomposition
methods and other hierarchical approaches for realistic system sizes can be
achieved.Comment: Additional comparison to method of arXiv:1011.2775 and to
mixed-precision odd-even preconditioned BiCGStab. Results of numerical
experiments changed slightly due to more systematic use of odd-even
preconditionin
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