Low rank iterative methods for projected generalized Lyapunov equations

By Tatjana Stykel. 2005

98 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d1acdac36bb30d801f9c13a9adda9e48cf285eb2

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Citations in the corpus

Gramian-Based Reduction Method Applied to Large Sparse Power System Descriptor Models (2008, methodology): “Gramian-based approaches using singular or descriptor systems have also been developed [16]–[18], but result expensive for power system applications.”
Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form (2005, background): “where Spf(E; A) denotes the nite spectrum of the pencil E A, see [ 75 ].The computation of the optimal shift parameters is a dicult problem, since the nite eigenvalues of the pencil E A (in particular if it is large and sparse) are in general unknown and expensive to compute).”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “Projection-based model reduction of DAEs has been studied extensively; see, for example, [45, 50, 118, 129, 172, 195, 208, 209].”
Krylov subspace methods for projected Lyapunov equations (2012, methodology): “Finally, several iterative methods such as the alternating direction implicit (ADI) method [5, 22, 23, 25], the cyclic Smith method [11, 25] and Krylov subspace type methods [14, 16, 17, 19, 28, 32] have been developed for large-scale Lyapunov equations over the last twenty years.”
A Structure Preserving FGMRES Method for Solving Large Lyapunov Equations (2012, methodology): “We have tested our method on several examples from NEC Europe and compared the solution with the state of the art method LRCF-ADI as stand-alone solver for the associated generalized, projected Lyapunov equations [9].”