Minimal residual methods augmented with eigenvectors for solving Sylvester equations and generalized Sylvester equations

DOI10.1016/j.amc.2005.12.055zbMath1148.65029OpenAlexW2039302627MaRDI QIDQ945392

Yi-Qin Lin

Publication date: 12 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.12.055

zbMATH Keywords

minimal residual methodKrylov subspaceRitz vectorRitz valueaugmented Arnoldi process

Mathematics Subject Classification ID

Related Items (10)

An efficient algorithm for solving general coupled matrix equations and its application ⋮ A modified gradient based algorithm for solving Sylvester equations ⋮ Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations ⋮ An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation ⋮ An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations ⋮ The relaxed gradient based iterative algorithm for the symmetric (skew symmetric) solution of the Sylvester equation \(A X + X B = C\) ⋮ On the sinc-Galerkin method for triharmonic boundary-value problems ⋮ On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations ⋮ On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations ⋮ Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• Controllability, observability and the solution of AX-XB=C
• SOR for \(AX-XB=C\)
• Krylov-subspace methods for the Sylvester equation
• Nonsingular solutions of TA-BT=C
• Global FOM and GMRES algorithms for matrix equations
• Krylov subspace methods for the generalized Sylvester equation
• Projection methods for large Lyapunov matrix equations
• Implicitly restarted global FOM and GMRES for nonsymmetric matrix equations and Sylvester equations
• Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
• The optimal projection equations for fixed-order dynamic compensation
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Hessenberg-Schur method for the problem AX + XB= C
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• A Restarted GMRES Method Augmented with Eigenvectors
• Harmonic projection methods for large non-symmetric eigenvalue problems
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Block Krylov subspace methods for solving large Sylvester equations

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