A single-step iteration method for non-Hermitian positive definite linear systems
type: Item
instance of: scholarly article
title: A single-step iteration method for non-Hermitian positive definite linear systems
zbMATH Open document ID: 1404.65019
author: Xiang Wang
author: Xiaoyong Xiao
author: Qing-Qing Zheng
published in: Journal of Computational and Applied Mathematics
publication date: 2018-11-16T00:00:00Z
review text: The document presents a new iterative method based on a generalized version of the splitting used in HSS (Hermitian and skew-Hermitian splitting). The authors consider a particular instantiation of the general framework described and study the conditions for convergence. They then proceed to find the optimal parameter and support the theories with numerical experiments, where they confront the new method with famous and different frameworks.
reviewed by: Giovanni Barbarino
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F08
zbMATH DE Number: 6980362
zbMATH Keywords: convergence theory
zbMATH Keywords: matrix splitting
zbMATH Keywords: preconditioner
zbMATH Keywords: numerical experiment
zbMATH Keywords: stationary iterative method
MaRDI profile type: Publication
full work available at URL: j.cam.2018.07.021
OpenAlex ID: W2884600692
cites work: Optical tomography in medical imaging
cites work: Efficient preconditioning for sequences of parametric complex symmetric linear systems
cites work: Q4814506
cites work: Q1594604
cites work: Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models.
cites work: Q5689624
cites work: Parallel iterative methods for sparse linear systems
cites work: A COCR method for solving complex symmetric linear systems
cites work: Several variants of the Hermitian and skew-Hermitian splitting method for a class of complex symmetric linear systems
cites work: Q4947421
cites work: New Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems
cites work: Alternating-directional PMHSS iteration method for a class of two-by-two block linear systems
cites work: Block preconditioners for complex symmetric linear system with two-by-two block form
cites work: Inexact splitting-based block preconditioners for block two-by-two linear systems
cites work: A note on preconditioners for complex linear systems arising from PDE-constrained optimization problems
cites work: Q5639278
cites work: Q4113326
cites work: A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
cites work: Schur complement-based domain decomposition preconditioners with low-rank corrections
cites work: An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices
cites work: A Rational Function Preconditioner For Indefinite Sparse Linear Systems
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: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems
cites work: Efficient single-step preconditioned HSS iteration methods for complex symmetric linear systems
cites work: A new single-step iteration method for solving complex symmetric linear systems
cites work: A modified GPSS method for non-Hermitian positive definite linear systems
cites work: On positive-definite and skew-Hermitian splitting iteration methods for continuous Sylvester equation \(AX+XB=C\)
cites work: On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation \(AXB=C\)
cites work: On a Hermitian and skew-Hermitian splitting iteration method for continuous Sylvester equations
cites work: A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations
cites work: A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation AXB = C
cites work: Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C
cites work: Q3410058
cites work: A Generalization of the Hermitian and Skew-Hermitian Splitting Iteration
cites work: On preconditioned MHSS iteration methods for complex symmetric linear systems
cites work: A block alternating splitting iteration method for a class of block two-by-two complex linear systems
cites work: A single-step HSS method for non-Hermitian positive definite linear systems
cites work: A parameterized SHSS iteration method for a class of complex symmetric system of linear equations
cites work: Modified HSS iteration methods for a class of complex symmetric linear systems
cites work: Matrix Preconditioning Techniques and Applications
cites work: A new SOR-like method for the saddle point problems
cites work: A shift-splitting preconditioner for a class of block two-by-two linear systems
DOI: 10.1016/J.CAM.2018.07.021
description: scientific article; zbMATH DE number 6980362