A quadrature framework for solving Lyapunov and Sylvester equations
| Autor: | Heike Faßbender, Christian Bertram |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Lyapunov function
Numerical Analysis Algebra and Number Theory Rank (linear algebra) Approximations of π 010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics Residual 01 natural sciences Mathematics::Numerical Analysis Quadrature (mathematics) Numerical integration symbols.namesake Ordinary differential equation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Discrete Mathematics and Combinatorics Applied mathematics Geometry and Topology 0101 mathematics Equivalence (measure theory) Mathematics |
| Zdroj: | Linear Algebra and its Applications. 622:66-103 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2021.03.029 |
| Popis: | This paper introduces a novel framework for the solution of (large-scale) Lyapunov and Sylvester equations derived from numerical integration methods. Suitable systems of ordinary differential equations are introduced. Low rank approximations of their solutions are produced by Runge-Kutta methods. Appropriate Runge-Kutta methods are identified following the idea of geometric numerical integration to preserve a geometric property, namely a low rank residual. For both types of equations we prove the equivalence of one particular instance of the resulting algorithm to the well known ADI iteration. |
| Databáze: | OpenAIRE |
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