Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations

DOI10.1007/s12190-019-01278-7zbMath1505.65196OpenAlexW2968573015MaRDI QIDQ2053275

Hamad Talibi Alaoui, Lakhlifa Sadek, Abdeslem Hafid Bentbib, El M. Sadek

Publication date: 29 November 2021

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

Full work available at URL: https://doi.org/10.1007/s12190-019-01278-7

zbMATH Keywords

matrix exponentiallow-rank approximationdifferential Sylvester equationsextended global Krylov subspaces

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical linear algebra (65F99) Numerical computation of matrix exponential and similar matrix functions (65F60) Numerical methods for matrix equations (65F45)

Related Items (7)

The extended block Arnoldi method for solving generalized differential Sylvester equations ⋮ Fractional BDF methods for solving fractional differential matrix equations ⋮ Numerical methods for solving large-scale systems of differential equations ⋮ Structure preserving subspace methods for the general coupled discrete-time periodic matrix equation and its application in antilinear periodic system ⋮ A numerical approach based on Bernstein collocation method: application to differential Lyapunov and Sylvester matrix equations ⋮ The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients ⋮ A class of fixed point iteration for the coupled algebraic Riccati equation

Uses Software

• SparseMatrix
• LYAPACK
• MATLAB expm
• Algorithm 432

Cites Work

• A minimal residual norm method for large-scale Sylvester matrix equations
• Extended Arnoldi methods for large low-rank Sylvester matrix equations
• Recursion relations for the extended Krylov subspace method
• ADI preconditioned Krylov methods for large Lyapunov matrix equations
• On the ADI method for Sylvester equations
• Matrix Riccati equations in control and systems theory
• Numerical low-rank approximation of matrix differential equations
• Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations
• Numerical solutions to large-scale differential Lyapunov matrix equations
• On some Krylov subspace based methods for large-scale nonsymmetric algebraic Riccati problems
• On the benefits of the \(L D L^T\) factorization for large-scale differential matrix equation solvers
• On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations
• A note on the numerical approximate solutions for generalized Sylvester matrix equations with applications
• Low rank approximate solutions to large Sylvester matrix equations
• Convergence properties of some block Krylov subspace methods for multiple linear systems
• Low-Rank Second-Order Splitting of Large-Scale Differential Riccati Equations
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Some general implicit processes for the numerical solution of differential equations
• A Hessenberg-Schur method for the problem AX + XB= C
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• 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
• Computational Krylov‐based methods for large‐scale differential Sylvester matrix problems
• Iterative Krylov Methods for Large Linear Systems
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Rosenbrock Methods for Solving Riccati Differential Equations
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Numerical Methods for Ordinary Differential Equations
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