Projection methods for large Lyapunov matrix equations

By Khalide Jbilou, A. J. Riquet. 2006

150 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/63bf99bd7a4bc8e514367eb02c0c0c51e0709623

How researchers see this paper

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In Computational Theory and Mathematics

1. Valeria Simoncini
2. Peter Benner
3. Bart Vandereycken
4. Stefan Vandewalle
5. Tatjana Stykel
6. Ulrike Baur
7. Lihong Feng
8. André Uschmajew

In Control and Systems Engineering

1. Valeria Simoncini
2. Tatjana Stykel
3. Peter Benner
4. Stefan Vandewalle
5. Bart Vandereycken
6. Ulrike Baur
7. Lihong Feng
8. Elena Virnik

In Statistical and Nonlinear Physics

1. Valeria Simoncini
2. Peter Benner
3. Bart Vandereycken
4. Tatjana Stykel
5. Stefan Vandewalle
6. Ulrike Baur
7. Lihong Feng
8. Jens Saak

Citations in the corpus

• Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “, • Krylov subspace methods [188, 67, 68, 111, 113, 114, 116, 118, 136, 171, 179, 180], and tensor Krylov subspace methods [31, 124], • the factorized sign function iteration [34, 42, 43], and data-sparse implementations of the method [22, 24, 99], • multi-grid methods [152, 167], based on low-rank ”
• A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations (2010, methodology): “Some of these solvers are based on either the ADI or Smith method (see [37], [31], and [20]); on Krylov subspace techniques (see [39], [24], [25], and [42]); or on low-rank arithmetic (see [19]).”
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations (2007, unknown): “, [23], [24], [25], [26], [28], [32], and the general treatment in [1].”
• Krylov subspace methods for projected Lyapunov equations (2012, methodology): “In particular, we consider the block and global Krylov subspace methods [16, 19], the extended Krylov subspace method [32], a combination of them [14], and also recently developed preconditioning with the classical ADI method [17].”
• Computational Methods for Linear Matrix Equations (2016, methodology): “The Global Krylov subspace method for the Sylvester equation was applied to the Lyapunov equation in [145], with natural simplifications due to the fact that one single space needs to be generated; numerical experiments in [145] showed better performance than the standard block Krylov subspace metho”