A Note on the Superlinear Convergence of GMRES
From MaRDI portal
Publication:4337451
DOI10.1137/S0036142993259792zbMath0873.65054OpenAlexW2015953024MaRDI QIDQ4337451
Publication date: 9 October 1997
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s0036142993259792
Hilbert spacesingular valueslinear operator equationKrylov subspace methodssuperlinear convergencecompact operatorsgeneralized minimal residual methoddegree of compactnessGMRES methods
Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)
Related Items
Discrete krylov subspace methods for equations of the second kind, Preconditioning Methods for Thin Scattering Structures Based on Asymptotic Results, Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations, On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions, Convergence of Krylov subspace solvers with Schwarz preconditioner for the exterior Maxwell problem, Convergence estimates for solution of integral equations with GMRES, Embedded techniques for choosing the parameter in Tikhonov regularization, A GCV based Arnoldi-Tikhonov regularization method, Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners, Integral equation methods for the Morse-ingard equations, A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems, GMRES algorithms over 35 years, Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks, Performance of iterative solvers for acoustic problems. II: Acceleration by ILU-type preconditioner., Krylov subspace methods for estimating operator-vector multiplications in Hilbert spaces, Bi-parametric operator preconditioning, Some transpose-free CG-like solvers for nonsymmetric ill-posed problems, Scaling, reordering, and diagonal pivoting in ILU preconditionings, Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems, Direct methods and ADI‐preconditioned Krylov subspace methods for generalized Lyapunov equations, Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation, Convergence analysis of Krylov subspace methods, Q-superlinear convergence of the GMRES algorithm for multi-materials with strong interface, Robust projection method for Fredholm integral equation of the second kind, Comments on the GMRES Convergence for Preconditioned Systems, Simultaneous solution of large-scale linear systems and eigenvalue problems with a parallel GMRES method, Preconditioning the EFIE on screens, Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems, Convergence bounds of GMRES with Schwarz' preconditioner for the scattering problem, Discrete QMR and BCG in the numerical solution of linear systems of ODEs, Stability of Linear GMRES Convergence with Respect to Compact Perturbations, Some Properties of the Arnoldi-Based Methods for Linear Ill-Posed Problems