Global quasi-minimal residual method for the Sylvester equations

DOI10.1007/s11741-007-0109-yzbMath1142.65342OpenAlexW2062847111MaRDI QIDQ5436237

Guiding Gu, Yong Wang

Publication date: 14 January 2008

Published in: Journal of Shanghai University (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11741-007-0109-y

zbMATH Keywords

numerical resultsSylvester equationsGMRES methodsgeneralized minimal residualglobal Krylov subspace methodglobal quasi-minimal residual (QMR) method

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10)

Related Items

Deflated and augmented global Krylov subspace methods for the matrix equations, A shifted complex global Lanczos method and the quasi-minimal residual variant for the Stein-conjugate matrix equation \(X + A \overline{X} B = C\), Global GPBiCGstab\((L)\) method for solving linear matrix equations

Uses Software

• Algorithm 432

Cites Work

• Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment
• Krylov-subspace methods for the Sylvester equation
• Linear and numerical linear algebra in control theory: Some research problems
• A convergence analysis of GMRES and FOM methods for Sylvester equations
• Global FOM and GMRES algorithms for matrix equations
• A Hessenberg-Schur method for the problem AX + XB= C
• On the solution of large Sylvester‐observer equations
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides
• Block Krylov subspace methods for solving large Sylvester equations