On spectral clustering of HSS preconditioner for generalized saddle-point matrices

DOI10.1016/j.laa.2018.06.022zbMath1398.65036OpenAlexW2808724796MaRDI QIDQ1654401

Zhong Zhi Bai

Publication date: 8 August 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.06.022

zbMATH Keywords

preconditioningspectral propertyHermitian and skew-Hermitian splittinggeneralized saddle-point problem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (13)

Additive Inexact Block Triangular Preconditioners for Saddle Point Problems Arising in Meshfree Discretization of Piezoelectric Equations ⋮ On the preconditioning properties of RHSS preconditioner for saddle-point linear systems ⋮ Two-parameter block triangular splitting preconditioner for block two-by-two linear systems ⋮ Regularized DPSS preconditioners for generalized saddle point linear systems ⋮ On the regularization matrix of the regularized DPSS preconditioner for non-Hermitian saddle-point problems ⋮ Convergence analysis for modified PAHSS-PU method with new parameter setting ⋮ On the convergence of the minimum residual HSS iteration method ⋮ ERHSS iteration method for PDE optimal control problem ⋮ Newton-PGSS and its improvement method for solving nonlinear systems with saddle point Jacobian matrices ⋮ A block positive-semidefinite splitting preconditioner for generalized saddle point linear systems ⋮ A class of modified DPSS preconditioners for generalized saddle-point linear systems ⋮ Spectral analysis of the matrix splitting preconditioner for block two-by-two linear systems ⋮ A two-parameter shift-splitting preconditioner for saddle point problems

Cites Work

• Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks
• Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems
• Motivations and realizations of Krylov subspace methods for large sparse linear systems
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• On nonsingularity of block two-by-two matrices
• Optimal parameters in the HSS-like methods for saddle-point problems
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices
• Numerical solution of saddle point problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Fast Iterative Solution of Stabilised Stokes Systems. Part I: Using Simple Diagonal Preconditioners
• Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
• A Preconditioner for Generalized Saddle Point Problems
• Spectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems
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