A low-order block preconditioner for saddle point linear systems
type: Item
instance of: scholarly article
title: A low-order block preconditioner for saddle point linear systems
zbMATH Open document ID: 1427.65043
published in: Computational and Applied Mathematics
publication date: 2018-08-02T00:00:00Z
review text: The paper considers solution of large sparse saddle point problems. A new preconditioner for Krylov subspace methods (e.g. GMRES) is proposed, based on describing formally the system matrix as a 3 by 3 block structured one. Then, some spectral properties of the preconditioned matrix are derived. In particular, eigenvalue distribution is studied. Furthermore, an upper bound for the degree of the minimal polynomial is provided. Based on the numerical examples, the new preconditioner can outperform other preconditioners such as HSS, RHSS, etc.
reviewed by: Iveta Hnetynkova
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6912498
zbMATH Keywords: saddle point problem
zbMATH Keywords: block preconditioner
zbMATH Keywords: eigenvalue distribution
author: Yi-Fen Ke
author: Changfeng Ma
MaRDI profile type: Publication
full work available at URL: s40314-017-0432-2
OpenAlex ID: W2592720350
cites work: Q3266142
cites work: Optimal parameters in the HSS-like methods for saddle-point problems
cites work: On SSOR‐like preconditioners for non‐Hermitian positive definite matrices
cites work: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems
cites work: On Inexact Preconditioners for Nonsymmetric Matrices
cites work: On parameterized inexact Uzawa methods for generalized saddle point problems
cites work: Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
cites work: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems
cites work: A Preconditioner for Generalized Saddle Point Problems
cites work: Numerical solution of saddle point problems
cites work: Finite elements. Theory, fast solvers, and applications in solid mechanics. Transl. from the German by Larry L. Schumaker.
cites work: Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
cites work: Uzawa type algorithms for nonsymmetric saddle point problems
cites work: Mixed and Hybrid Finite Element Methods
cites work: Fast Uzawa algorithms for solving non‐symmetric stabilized saddle point problems
cites work: A class of Uzawa-PSS iteration methods for nonsingular and singular non-Hermitian saddle point problems
cites work: A Relaxed HSS Preconditioner for Saddle Point Problems from Meshfree Discretization
cites work: A class of generalized shift-splitting preconditioners for nonsymmetric saddle point problems
cites work: A generalization of the inexact parameterized Uzawa methods for saddle point problems
cites work: A generalized shift-splitting preconditioner for singular saddle point problems
cites work: On the Nonlinear Inexact Uzawa Algorithm for Saddle-Point Problems
cites work: The inexact Uzawa algorithm for saddle point problem
cites work: An Inexact Uzawa-Type Iterative Method For Solving Saddle Point Problems
cites work: A sufficient condition for the convergence of the inexact Uzawa algorithm for saddle point problems
cites work: Analysis of iterative algorithms of Uzawa type for saddle point problems
cites work: Symmetric SOR method for augmented systems
cites work: Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
cites work: Q5702543
cites work: Q3321366
cites work: SOR-like methods for augmented systems
cites work: Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems
cites work: An inexact relaxed DPSS preconditioner for saddle point problem
cites work: Spectrum analysis of a more general augmentation block preconditioner for generalized saddle point matrices
cites work: ILU Preconditioners for Nonsymmetric Saddle-Point Matrices with Application to the Incompressible Navier--Stokes Equations
cites work: Eigenvalue analysis of the SIMPLE preconditioning for incompressible flow
cites work: A relaxed splitting preconditioner for saddle point problems
cites work: Preconditioned Hss-Like Iterative Method for Saddle Point Problems
cites work: Q5467103
cites work: Iterative Krylov Methods for Large Linear Systems
cites work: Optimization of the parameterized Uzawa preconditioners for saddle point matrices
cites work: Improved PHSS iterative methods for solving saddle point problems
cites work: Preconditioning
cites work: Q4016509
cites work: Q5691079
cites work: A modified SSOR iterative method for augmented systems
cites work: The Uzawa-HSS method for saddle-point problems
cites work: A relaxed positive-definite and skew-Hermitian splitting preconditioner for saddle point problems
cites work: On HSS-based constraint preconditioners for generalized saddle-point problems
cites work: On HSS-based sequential two-stage method for non-Hermitian saddle point problems
DOI: 10.1007/S40314-017-0432-2
description: scientific article; zbMATH DE number 6912498