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A quadrature framework for solving Lyapunov and Sylvester equations.
- Source :
-
Linear Algebra & its Applications . Aug2021, Vol. 622, p66-103. 38p. - Publication Year :
- 2021
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SYLVESTER matrix equations
*NUMERICAL integration
*RUNGE-Kutta formulas
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 622
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 150083405
- Full Text :
- https://doi.org/10.1016/j.laa.2021.03.029