A note on preconditioned GMRES for solving singular linear systems

DOI10.1007/s10543-009-0247-7zbMath1186.65040OpenAlexW2032062290MaRDI QIDQ2379355

Naimin Zhang

Publication date: 19 March 2010

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-009-0247-7

zbMATH Keywords

numerical examplespreconditioninggeneralized minimal residual (GMRES) methodsingular linear systemproper splittingsrange-symmetric

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (15)

Multistep matrix splitting iteration preconditioning for singular linear systems ⋮ DGMRES method augmented with eigenvectors for computing the Drazin-inverse solution of singular linear systems ⋮ A triple-parameter modified SSOR method for solving singular saddle point problems ⋮ Modified parameterized inexact Uzawa method for singular saddle-point problems ⋮ Semi-convergence analysis of preconditioned deteriorated PSS iteration method for singular saddle point problems ⋮ On GMRES for Singular EP and GP Systems ⋮ On the preconditioned MINRES method for solving singular linear systems ⋮ Convergence analysis of modified PGSS methods for singular saddle-point problems ⋮ Analysis of the relaxed deteriorated PSS preconditioner for singular saddle point linear systems ⋮ Convergence of a generalized PMHSS method for a class of singular block two-by-two linear systems ⋮ Semi-convergence analysis of Uzawa methods for singular saddle point problems ⋮ An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index ⋮ Convergence behavior of generalized parameterized Uzawa method for singular saddle-point problems ⋮ How to compute the minimum norm least squares solution of singular linear system by using the preconditioned HSS method? ⋮ Augmented block splitting preconditioner for singular saddle point problems

Uses Software

• DGMRES

Cites Work

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• Inexact GMRES for singular linear systems
• On the solution of singular linear systems of algebraic equations by semiiterative methods
• GMRES-type methods for inconsistent systems
• Some results about GMRES in the singular case
• Spectral behaviour of GMRES applied to singular systems
• The Idea behind Krylov Methods
• GMRES On (Nearly) Singular Systems
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• Numerical solution of saddle point problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Proper Splittings of Rectangular Matrices
• Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
• Constraint Preconditioning for Indefinite Linear Systems
• A Note on Constraint Preconditioning for Nonsymmetric Indefinite Matrices
• Breakdown-free GMRES for Singular Systems
• DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems

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