A non-alternating preconditioned HSS iteration method for non-Hermitian positive definite linear systems

2015 ◽  
Vol 36 (1) ◽  
pp. 367-381 ◽  
Author(s):  
Yu-Jiang Wu ◽  
Xu Li ◽  
Jin-Yun Yuan
Keyword(s):  
Linear Systems ◽  
Iteration Method ◽  
Positive Definite ◽  
Hss Iteration ◽  
Hss Iteration Method

scholarly journals A Generalized HSS Iteration Method for Continuous Sylvester Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xu Li ◽  
Yu-Jiang Wu ◽  
Ai-Li Yang ◽  
Jin-Yun Yuan
Keyword(s):  
Iteration Method ◽  
Iterative Process ◽  
Convergence Property ◽  
Computational Cost ◽  
Positive Definite ◽  
Parameter Region ◽  
Hss Iteration ◽  
Region Of Convergence ◽  
Iteration Technique ◽  
Hss Iteration Method

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the iterative process. An exact parameter region of convergence for the method is strictly proved and a minimum value for the upper bound of the iterative spectrum is derived. Moreover, to reduce the computational cost, we establish an inexact variant of the GHSS (IGHSS) iteration method whose convergence property is discussed. Numerical experiments illustrate the efficiency and robustness of the GHSS iteration method and its inexact variant.

scholarly journals The Picard-HSS-SOR iteration method for absolute value equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lin Zheng
Keyword(s):  
Iteration Method ◽  
Numerical Experiments ◽  
Absolute Value Equation ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Convergence Results ◽  
Hss Iteration ◽  
The Absolute ◽  
Hss Iteration Method

AbstractIn this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergence results of the Picard-HSS-SOR iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments demonstrate that the Picard-HSS-SOR iteration method for solving absolute value equations is feasible and effective.

Sign in / Sign up

Export Citation Format

Share Document