Comments on the GMRES Convergence for Preconditioned Systems

DOI10.1007/978-3-540-78827-0_4zbMath1229.65063OpenAlexW1518887724MaRDI QIDQ3616803

Bernard Philippe, Nabil Gmati

Publication date: 26 March 2009

Published in: Large-Scale Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-78827-0_4

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Orthogonalization in numerical linear algebra (65F25) Preconditioners for iterative methods (65F08)

Related Items (6)

Band-times-circulant preconditioners for non-symmetric Toeplitz systems ⋮ Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation ⋮ Convergence of Krylov subspace solvers with Schwarz preconditioner for the exterior Maxwell problem ⋮ Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency? ⋮ Schwarz method justification of a coupling between finite elements and integral representation for Maxwell exterior problem ⋮ Finite Elements for Helmholtz Equations with a Nonlocal Boundary Condition

Cites Work

• Numerical range, GMRES and Faber polynomials.
• On acceleration methods for coupled nonlinear elliptic systems
• On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block
• On handling the boundary conditions at infinity for some exterior problems by the alternating Schwarz method
• An explicit formulation of the multiplicative Schwarz preconditioner
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• On the Coupling of Boundary Integral and Finite Element Methods
• A Note on the Superlinear Convergence of GMRES
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

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