scholarly journals On the Global Linear Convergence of the ADMM with MultiBlock Variables

2015 ◽  
Vol 25 (3) ◽  
pp. 1478-1497 ◽  
Author(s):  
Tianyi Lin ◽  
Shiqian Ma ◽  
Shuzhong Zhang
Keyword(s):  
Linear Convergence ◽  
Global Linear Convergence

scholarly journals A Three-Step Iterative Method for Solving Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jing-Mei Feng ◽  
San-Yang Liu
Keyword(s):  
Nonlinear Equation ◽  
Quadratic Convergence ◽  
Linear Convergence ◽  
Singular Values ◽  
System Of Nonlinear Equations ◽  
Absolute Value Equations ◽  
Local Quadratic Convergence ◽  
Absolute Value ◽  
Global Linear Convergence ◽  
Step Algorithm

In this paper, we transform the problem of solving the absolute value equations (AVEs) Ax−x=b with singular values of A greater than 1 into the problem of finding the root of the system of nonlinear equation and propose a three-step algorithm for solving the system of nonlinear equation. The proposed method has the global linear convergence and the local quadratic convergence. Numerical examples show that this algorithm has high accuracy and fast convergence speed for solving the system of nonlinear equations.

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