Numerical methods for differential linear matrix equations via Krylov subspace methods

DOI10.1016/j.cam.2019.112674zbMath1493.65078arXiv1805.10192OpenAlexW2997749859MaRDI QIDQ2297107

M. Hached, Khalide Jbilou

Publication date: 18 February 2020

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.10192

zbMATH Keywords

Lyapunov equationSylvester equationmatrix Krylov subspaceglobal Arnoldi

Mathematics Subject Classification ID

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

Related Items (2)

Common solutions to the matrix equations \(AX=B\) and \(XC=D\) on a subspace ⋮ Galerkin trial spaces and Davison-Maki methods for the numerical solution of differential Riccati equations

Uses Software

• MATLAB expm
• mftoolbox
• Algorithm 432

Cites Work

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• Extended Arnoldi methods for large low-rank Sylvester matrix equations
• Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices
• An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation
• Matrix Riccati equations in control and systems theory
• Global FOM and GMRES algorithms for matrix equations
• Numerical solutions to large-scale differential Lyapunov matrix equations
• Convergence properties of some block Krylov subspace methods for multiple linear systems
• A Computational Method for Symmetric Stein Matrix Equations
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• A Hessenberg-Schur method for the problem AX + XB= C
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Functions of Matrices

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