The Sylvester equation and approximate balanced reduction

By Danny C. Sorensen, Athanasios C. Antoulas. 2002

233 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c405abb1a25fe7d891bf678a73b3176266eaede6

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In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

The global modal parameterization for non‐linear model‐order reduction in flexible multibody dynamics (2007, methodology): “Balanced truncation methods [8–10] rely on a singular value decomposition, and they lead to a reduced-order model with an a priori bound”
Model reduction of large-scale systems by least squares (2006, unknown): “Given the full-order model as in (1.1), we expand the transfer function G(s) = c(sI − A)−1b + d about a point σ ∈ C in the complex plane which is not a pole of : G(s)= c(σI − A− (σ − s)I )−1b + d = c(I − (σI − A)−1(σ − s))−1(σI − A)−1b + d = η(0)σ + η(1)σ (σ − s)+ η(2)σ (σ − s)2 + η(3)σ (σ − s)3 +…”
A Survey of Model Reduction by Balanced Truncation and Some New Results (2004, background): “We refer the reader to [23], [5], [6], [34], [35], [41] and the references therein for further information on these issues.”
Model reduction of second order systems (2005, background): “Recent work by Antoulas and Sorensen considers this problem and describes an Approximate Balanced Truncation approach for large-scale linear systems [15].”
Computational Methods for Linear Matrix Equations (2016, background): “For B1, B2 having a single column, or for A symmetric and B1, B2 such that B > 2 (zI−A)B1 is symmetric, it is possible to show that W(2) = PQ, so that the eigenvalues of W coincide with the square root of the eigenvalues of PQ [89],[242].”
Hessian‐based model reduction for large‐scale systems with initial‐condition inputs (2008, methodology): “Methods to compute the basis in the largescale setting include Krylov-subspace methods [15, 16, 19], approximate balanced truncation [20,27,28,31], and proper orthogonal decomposition (POD) [13,24,30].”
A real quaternion matrix equation with applications (2013, unknown): “[19,21]).”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “Model reduction based on the cross-Gramian is also considered in [6,23,182].”