scholarly journals Multigrid methods for block‐Toeplitz linear systems: convergence analysis and applications

2020 ◽  
Author(s):  
Marco Donatelli ◽  
Paola Ferrari ◽  
Isabella Furci ◽  
Stefano Serra‐Capizzano ◽  
Debora Sesana
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Multigrid Methods

A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

2017 ◽  
Vol 7 (4) ◽  
pp. 827-836
Author(s):  
Ze-Jia Xie ◽  
Xiao-Qing Jin ◽  
Zhi Zhao
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
Indefinite Systems ◽  
Indefinite Linear Systems ◽  
Theoretical Results

AbstractSome convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

scholarly journals Two-step Tensor Splitting Iteration Method for Multi-linear Systems

2021 ◽  
pp. 48-55
Author(s):  
Bing Cheng ◽  
Guangbin Wang ◽  
Fuping Tan
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Iteration Method ◽  
New Method ◽  
Numerical Examples ◽  
Splitting Iteration Method

In this paper, we construct two-step tensor splitting iteration method for multi-linear systems. Moreover, we present convergence analysis of this method. Finally, we give two numerical examples to show that this new method is more ecient than the existing methods.

Sign in / Sign up

Export Citation Format

Share Document