On parameterized inexact Uzawa methods for generalized saddle point problems

DOI10.1016/j.laa.2008.01.018zbMath1144.65020OpenAlexW2026635066MaRDI QIDQ924363

Zeng-Qi Wang, Zhong Zhi Bai

Publication date: 15 May 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.01.018

zbMATH Keywords

algorithmconvergencegeneralized saddle point problemparametrized inexact Uzawa methodacceleration techniquequasi-optimal convergence factorquasi-optimal relaxation parameter

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10)

Related Items (only showing first 100 items - show all)

A GPIU method for fractional diffusion equations ⋮ On parameterized matrix splitting preconditioner for the saddle point problems ⋮ On SSOR-like preconditioner for saddle point problems with dominant skew-Hermitian part ⋮ The improvements of the generalized shift-splitting preconditioners for non-singular and singular saddle point problems ⋮ A note on block-diagonally preconditioned PIU methods for singular saddle point problems ⋮ Class of Uzawa-NPHSS iteration method for solving nonsingular and singular saddle point problems ⋮ Structured backward error analysis for a class of block three-by-three saddle point problems ⋮ Modified bas iteration method for absolute value equation ⋮ On Uzawa-SSI method for non-Hermitian saddle point problems ⋮ A splitting preconditioner for saddle point problems ⋮ On the generalized AOR and CG iteration methods for a class of block two-by-two linear systems ⋮ Improved CRI iteration methods for a class of complex symmetric linear systems ⋮ A generalization of the inexact parameterized Uzawa methods for saddle point problems ⋮ On the iterative algorithm for saddle point problems ⋮ Optimal parameters of GSOR-like methods for solving the augmented linear systems ⋮ On GSOR-based iteration methods for solving weakly nonlinear systems with complex symmetric coefficient matrices ⋮ Additive Inexact Block Triangular Preconditioners for Saddle Point Problems Arising in Meshfree Discretization of Piezoelectric Equations ⋮ Backward and Forward Modified SOR Iteration Methods for Solving Standard Saddle-Point Problems ⋮ The corrected Uzawa method for solving saddle point problems ⋮ Modified modulus‐based matrix splitting iteration methods for linear complementarity problems ⋮ Application of modified homotopy perturbation method for solving the augmented systems ⋮ Preconditioned AHSS iteration method for singular saddle point problems ⋮ Unnamed Item ⋮ Parameterized preconditioned Hermitian and skew-Hermitian splitting iteration method for saddle-point problems ⋮ Semiconvergence of the extended PSS method for singular generalized saddle point problems ⋮ A parameterized shift-splitting preconditioner for saddle point problems ⋮ The block preconditioned \textit{LSQR} and \textit{GL}-\textit{LSQR} algorithms for the block partitioned matrices ⋮ Semi-convergence analysis of GMSSOR methods for singular saddle point problems ⋮ Modified Alternating Positive Semidefinite Splitting Preconditioner for Time-Harmonic Eddy Current Models ⋮ New variant of the HSS iteration method for weighted Toeplitz regularized least-squares problems from image restoration ⋮ On equivalence of three-parameter iterative methods for singular symmetric saddle-point problem ⋮ A simplified PSS preconditioner for non-Hermitian generalized saddle point problems ⋮ An inexact modified relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier-Stokes equations ⋮ A generalized variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems ⋮ An efficient preconditioned variant of the PSS preconditioner for generalized saddle point problems ⋮ An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems ⋮ A class of accelerated parameterized inexact Uzawa algorithms for complex symmetric linear systems ⋮ On quasi shift-splitting iteration method for a class of saddle point problems ⋮ On convergence and semi-convergence of SSOR-like methods for augmented linear systems ⋮ Preconditioned triangular splitting iteration method for a class of complex symmetric linear systems ⋮ A class of new extended shift-splitting preconditioners for saddle point problems ⋮ Minimum residual two-parameter TSCSP method for solving complex symmetric linear systems ⋮ Convergence analysis for modified PAHSS-PU method with new parameter setting ⋮ Convergence of a generalized MSSOR method for augmented systems ⋮ On hybrid preconditioning methods for large sparse saddle-point problems ⋮ Convergence analysis of modified PGSS methods for singular saddle-point problems ⋮ Combination of augmented Lagrangian technique and ST preconditioner for saddle point problems ⋮ Preconditioned accelerated generalized successive overrelaxation method for solving complex symmetric linear systems ⋮ A New GSOR Method for Generalised Saddle Point Problems ⋮ A Block Diagonal Preconditioner for Generalised Saddle Point Problems ⋮ On a New SSOR-Like Method with Four Parameters for the Augmented Systems ⋮ New Perturbation Bounds Analysis of a Kind of Generalized Saddle Point Systems ⋮ On the parameter selection in the transformed matrix iteration method ⋮ A note on parameterized block triangular preconditioners for generalized saddle point problems ⋮ On the GTSOR-like Method for the Augmented systems ⋮ Convergence analysis of the splitting-based iterative method for solving generalized saddle point problems ⋮ Modified two-step scale-splitting iteration method for solving complex symmetric linear systems ⋮ A general fast shift-splitting iteration method for nonsymmetric saddle point problems ⋮ A generalized preconditioned HSS method for singular saddle point problems ⋮ On generalized parameterized inexact Uzawa method for a block two-by-two linear system ⋮ Semi-convergence analysis of Uzawa methods for singular saddle point problems ⋮ Shift-splitting preconditioners for saddle point problems ⋮ General constraint preconditioning iteration method for singular saddle-point problems ⋮ On PSS-based constraint preconditioners for singular nonsymmetric saddle point problems ⋮ On semi-convergence of the generalized shift-splitting iteration method for singular nonsymmetric saddle point problems ⋮ Improved PPHSS iterative methods for solving nonsingular and singular saddle point problems ⋮ An accelerated symmetric SOR-like method for augmented systems ⋮ AOR-Uzawa iterative method for a class of complex symmetric linear system of equations ⋮ On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems ⋮ PMHSS iteration method and preconditioners for Stokes control PDE-constrained optimization problems ⋮ A modified parameterized shift-splitting preconditioner for saddle point problems ⋮ Accelerating the shift-splitting iteration algorithm ⋮ Efficient block splitting iteration methods for solving a class of complex symmetric linear systems ⋮ A relaxed deteriorated PSS preconditioner for nonsymmetric saddle point problems from the steady Navier-Stokes equation ⋮ Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems ⋮ Optimal parameters of the generalized symmetric SOR method for augmented systems ⋮ A note on semi-convergence of generalized parameterized inexact Uzawa method for singular saddle point problems ⋮ A class of upper and lower triangular splitting iteration methods for image restoration ⋮ Optimal accelerated SOR-like (ASOR) method for singular symmetric saddle point problems ⋮ A general Uzawa-type method for a class of \(2\times 2\) block structure linear system ⋮ Regularized preconditioned GMRES and the regularized iteration method ⋮ Modulus-based matrix splitting iteration methods for linear complementarity problems ⋮ A relaxed block-triangular splitting preconditioner for generalized saddle-point problems ⋮ Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems ⋮ An Accelerated SOR-Like Method for Generalised Saddle Point Problems ⋮ On parameterized block symmetric positive definite preconditioners for a class of block three-by-three saddle point problems ⋮ Analysis of relaxed nonlinear inexact Uzawa algorithm for symmetric saddle point problems ⋮ Generalized fast shift-splitting preconditioner for nonsymmetric saddle-point problems ⋮ Improved splitting preconditioner for double saddle point problems arising from liquid crystal director modeling ⋮ Preconditioned Richardson iteration for augmented linear systems ⋮ A modified ASOR-like method for augmented linear systems ⋮ A generalized shift-splitting preconditioner for saddle point problems ⋮ On preconditioning of double saddle point linear systems arising from liquid crystal director modeling ⋮ The Uzawa-HSS method for saddle-point problems ⋮ On parameter acceleration methods for saddle point problems ⋮ A new modified SSOR iteration method for solving augmented linear systems ⋮ A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling ⋮ Optimization of a parameterized inexact Uzawa method for saddle point problems ⋮ On generalized parameterized inexact Uzawa methods for singular saddle-point problems ⋮ The coupled iteration algorithms for computing PageRank

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A generalized successive overrelaxation method for least squares problems
• Minimum residual methods for augmented systems
• A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations
• Convergence for a general form of the GAOR method and its application to the MSOR method
• On the convergence of the generalized AOR method
• On the convergence of the MAOR method
• Preconditioning of elliptic problems by approximation in the transform domain
• Fast Uzawa algorithm for generalized saddle point problems
• Generalized extrapolation principle and convergence of some generalized iterative methods
• On generalized successive overrelaxation methods for augmented linear systems
• An Iterative Method with Variable Relaxation Parameters for Saddle-Point Problems
• Structured preconditioners for nonsingular matrices of block two-by-two structures
• Fast Uzawa algorithms for solving non‐symmetric stabilized saddle point problems
• Mixed and Hybrid Finite Element Methods
• Iterative Solution Methods
• Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
• Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
• Conjugate Gradient Methods for Toeplitz Systems
• Iterative Krylov Methods for Large Linear Systems
• On the convergence of the generalized matrix multisplitting relaxed methods
• On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis
• SOR-like methods for augmented systems
• Modified block SSOR preconditioners for symmetric positive definite linear systems

This page was built for publication: On parameterized inexact Uzawa methods for generalized saddle point problems