A NEW VERSION OF THE SMITH METHOD FOR SOLVING SYLVESTER EQUATION AND DISCRETE-TIME SYLVESTER EQUATION

DOI10.11948/2016040zbMath1463.65091OpenAlexW2195616778MaRDI QIDQ5121335

Ziya Mei, Xu Kong, Ji-Cheng Li

Publication date: 14 September 2020

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/2016040

zbMATH Keywords

convergencepositive definite matrixSylvester equationSmith methoddiscrete-time Sylvester equation

Mathematics Subject Classification ID

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

Related Items

New results of the IO iteration algorithm for solving Sylvester matrix equation

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations
• Cross-Gramian based model reduction for data-sparse systems
• On Smith-type iterative algorithms for the Stein matrix equation
• On the ADI method for Sylvester equations
• Iterative solution of the Lyapunov matrix equation
• Krylov-subspace methods for the Sylvester equation
• A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations
• Iterative methods for \(X-AXB=C\)
• On the generalized ADI method for the matrix equation \(X- AXB\)=\(C\)
• A convergence analysis of GMRES and FOM methods for Sylvester equations
• The Sylvester equation and approximate balanced reduction
• A note on Sylvester-type equations
• On modified HSS iteration methods for continuous Sylvester equations
• Krylov subspace methods for the generalized Sylvester equation
• Large-scale Stein and Lyapunov equations, Smith method, and applications
• Accurate solutions of \(M\)-matrix Sylvester equations
• On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations
• Efficient matrix-valued algorithms for solving stiff Riccati differential equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Alternating Direction Implicit Methods
• A Hessenberg-Schur method for the problem AX + XB= C
• Alternating Direction Implicit Iteration for Systems with Complex Spectra
• Numerical Integration of the Differential Riccati Equation and Some Related Issues
• Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
• How and Why to Solve the Operator Equation AX −XB = Y
• Application of ADI Iterative Methods to the Restoration of Noisy Images
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Matrix Equation $XA + BX = C$
• Approximation of Large-Scale Dynamical Systems
• Block Krylov subspace methods for solving large Sylvester equations