Preconditioned AHSS iteration method for singular saddle point problems

Authors:
Shan-Shan Wang;Guo-Feng Zhang
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000;School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000
Venue:
Numerical Algorithms
Year:
2013

Citing 9
Cited 1

Inexact and preconditioned Uzawa algorithms for saddle point problems

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems

SIAM Journal on Numerical Analysis
Practical methods for optimal control using nonlinear programming

Practical methods for optimal control using nonlinear programming
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems

SIAM Journal on Matrix Analysis and Applications
Weak-convergence theory of quasi-nonnegative splittings for singular matrices

Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems

Numerische Mathematik
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow

ACM Transactions on Mathematical Software (TOMS)
Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems

Journal of Computational and Applied Mathematics
On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems

Computing

A preconditioned GLHSS iteration method for non-Hermitian singular saddle point problems

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, for solving the singular saddle point problems, we present a new preconditioned accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration method. The semi-convergence of this method and the eigenvalue distribution of the preconditioned iteration matrix are studied. In addition, we prove that all eigenvalues of the iteration matrix are clustered for any positive iteration parameters 驴 and β. Numerical experiments illustrate the theoretical results and examine the numerical effectiveness of the AHSS iteration method served either as a preconditioner or as a solver.