Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems

By Zhong-Zhi Bai, Gene H. Golub. 2007

414 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b56aa4d5a523626969249451ff66e7c94a84e4d7

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In Atomic and Molecular Physics, and Optics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

A Relaxed HSS Preconditioner for Saddle Point Problems from Meshfree Discretization (2013, methodology): “The best known and the oldest methods are the Uzawa algorithm [14], the inexact Uzawa algorithms [9, 10, 18], the HSS (Hermitian and skew-Hermitian splitting) algorithms [1–3, 6, 13] and so on.”
Regularized HSS iteration methods for saddle-point linear systems (2017, methodology): “To improve the convergence rate of the HSS iteration method, Bai, Golub and Pan presented in [8] the preconditioned HSS (PHSS) iteration method by first preconditioning the saddle-point matrix A ∈ Cn×n and then iterating with the HSS iteration scheme, and Bai and Golub established in [4] the acceler”
A Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems (2013, methodology): “The method was extended to the solution of saddle point problems [12,13] and the idea of using two parameters to accelerate the HSS iteration method for solving saddle point linear systems was introduced in [6] and deeply discussed in [3].”
On preconditioned iteration methods for complex linear systems (2015, methodology): “The block two-by-two linear system (2) may be efficiently solved in real arithmetics by Krylov subspace iteration methods such as the preconditioned GMRES [18] and QMR [19–21], by alternating splitting iterationmethods such as PHSS [22] and PMHSS [13], or by C-to-R iterationmethods [17], for which h”
On semi-convergence of parameterized Uzawa methods for singular saddle point problems☆ (2009, background): “More related works can be found in [4,6,9,3].”