Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Methods

By John Sabino. 2006

125 citations recorded by the source corpus.

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Citations in the corpus

Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey (2013, background): “Several contributions [46, 25, 2, 51, 59] have investigated the singular value decay in X, especially in the Lyapunov case, in order to derive conditions on when a good approximation by low rank factors can be achieved.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “For eﬀective methods to solve large-scale Lyapunov equations, see, e.g., [46, 47, 152, 219] for ADI-type methods, [117, 191, 199, 206] for the Smith method and its variants, [78, 135, 203, 210] for Krylov-based methods, or the recent survey [48] and the references therein.”
Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations (2014, methodology): “the left and right eigenvectors coincide) (A, E), (F, G) in (18) it can be shown [37, 28, 23, 9] that optimal shifts for J iterations of Algorithm 2 have to satisfy the optimization problem”
On two numerical methods for the solution of large-scale algebraic Riccati equations (2014, background): “, [3], [45], for a more detailed analysis.”
A preconditioned low‐rank CG method for parameter‐dependent Lyapunov matrix equations (2014, background): “We start by recalling existing results [20, 28, 37] on the singular value decay of X(α) for fixed α ∈ [−1, 1].”
Towards an ADI iteration for Tensor Structured Equations (2014, methodology): “[27] J. Sabino, Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Method, PhD thesis, Rice University, Houston, Texas, June 2007. available from: http://www.caam.rice.edu/tech reports/2006/TR06-08.pdf.”
Low rank iterative methods for projected generalized Lyapunov equations (2005, methodology): “, [39], while the case of complex eigenvalues of is still not completely understood; see [18, 27, 32, 39] for some contributions.”
Krylov subspace methods for projected Lyapunov equations (2012, methodology): “Note that computing the normalized residuals η(Zk) even via the efficient methods proposed in [25, 30] can still be quite expensive for large-scale problems.”