Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
A flexible inner-outer preconditioned GMRES algorithm
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Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.
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Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
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Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.