Spectral properties of primal-based penalty preconditioners for saddle point problems
type: Item
instance of: scholarly article
title: Spectral properties of primal-based penalty preconditioners for saddle point problems
zbMATH Open document ID: 1186.65035
author: Shu-Qian Shen
author: Ting-Zhu Huang
author: Er-Jie Zhong
published in: Journal of Computational and Applied Mathematics
publication date: 2010-02-12T00:00:00Z
review text: A preconditioner for the system \[ \begin{pmatrix} A & B^T \cr B & -C \end{pmatrix} \begin{pmatrix} u \cr p \end{pmatrix} = b \] is obtained with an approximation \(\hat C\) of \(C\) and \(\hat S\) of the Schur complement \(S=A+B^T\hat C^{-1}B\). The method can be understood as follows: The matrix is rearranged \[ \begin{pmatrix} C & B \cr B^T & -A \end{pmatrix} \] and standard preconditioners are applied.
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5669150
zbMATH Keywords: saddle point problem
zbMATH Keywords: block preconditioner
zbMATH Keywords: eigenvalue
zbMATH Keywords: Krylov subspace method
reviewed by: D. Braess
describes a project that uses: IFISS
MaRDI profile type: Publication
full work available at URL: j.cam.2009.10.009
OpenAlex ID: W2058528845
cites work: A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
cites work: Quadratic finite elements and incompressible viscous flows
cites work: Fast Iterative Solution of Stabilised Stokes Systems. Part I: Using Simple Diagonal Preconditioners
cites work: A Preconditioned Iterative Method for Saddlepoint Problems
cites work: On optimization techniques for solving nonlinear inverse problems
cites work: Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
cites work: On Linear Least-Squares Problems with Diagonally Dominant Weight Matrices
cites work: Numerical solution of saddle point problems
cites work: A Primal-Based Penalty Preconditioner for Elliptic Saddle Point Systems
cites work: Preconditioning of Indefinite Problems by Regularization
cites work: Two preconditioners for saddle point problems in fluid flows
cites work: A class of iterative methods for solving saddle point problems
cites work: Q5691920
cites work: Analysis of iterative methods for saddle point problems: A unified approach
cites work: Block preconditioning for saddle point systems with indefinite (1, 1) block
cites work: Block triangular preconditioners for symmetric saddle-point problems
cites work: IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems
cites work: Parallel iterative methods for sparse linear systems
DOI: 10.1016/J.CAM.2009.10.009
description: scientific article; zbMATH DE number 5669150