Solution formulas for differential Sylvester and Lyapunov equations

DOI10.1007/s10092-019-0348-xzbMath1432.15015arXiv1811.08327OpenAlexW2982445066WikidataQ115214766 ScholiaQ115214766MaRDI QIDQ2302086

Peter Benner, Maximilian Behr, Jan Heiland

Publication date: 25 February 2020

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08327

zbMATH Keywords

low-rank methodsdifferential Lyapunov equationsdifferential Sylvester equations

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Numerical methods for matrix equations (65F45)

Related Items (10)

The extended block Arnoldi method for solving generalized differential Sylvester equations ⋮ Tracking control for the nonlinear complex dynamical network assisted with outgoing links dynamics ⋮ Multivariate self-exciting jump processes with applications to financial data ⋮ A numerical approach based on Bernstein collocation method: application to differential Lyapunov and Sylvester matrix equations ⋮ Averaging on macroscopic scales with application to Smoluchowski-Kramers approximation ⋮ The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients ⋮ Greedy algorithm for parameter dependent operator Lyapunov equations ⋮ Galerkin trial spaces and Davison-Maki methods for the numerical solution of differential Riccati equations ⋮ Lopsided DSS iteration method for solving complex Sylvester matrix equation ⋮ Computing the Lyapunov operator \(\varphi \)-functions, with an application to matrix-valued exponential integrators

Uses Software

• MESS
• mftoolbox

Cites Work

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• Functions of Matrices
• Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix
• Approximation of Large-Scale Dynamical Systems
• Functional analysis

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