Results 11 to 20 of about 133,110 (277)

A Three-Step Iterative Method for Solving Absolute Value Equations

Journal of Mathematics, 2020
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
Jing-Mei Feng, San-Yang Liu
doaj   +2 more sources

A New Finite-Difference Method for Nonlinear Absolute Value Equations

Mathematics
In this paper, we propose a new finite-difference method for nonconvex absolute value equations. The nonsmooth unconstrained optimization problem equivalent to the absolute value equations is considered.
Peng Wang, Yujing Zhang, Detong Zhu
doaj   +2 more sources

A new two-step iterative method for solving absolute value equations

Journal of Inequalities and Applications, 2019
We describe a new two-step iterative method for solving the absolute value equations Ax−|x|=b $Ax-|x|=b$, which is an NP-hard problem. This method is globally convergent under suitable assumptions.
Jingmei Feng, Sanyang Liu
doaj   +2 more sources

Modified HS conjugate gradient method for solving generalized absolute value equations

Journal of Inequalities and Applications, 2019
We investigate a kind of generalized equations involving absolute values of variables as |A|x−|B||x|=b $|A|x-|B||x|=b$, where A∈Rn×n $A \in R^{n\times n}$ is a symmetric matrix, B∈Rn×n $B \in R^{n\times n}$ is a diagonal matrix, and b∈Rn $b\in R^{n}$.
Ya Li, Shouqiang Du
doaj   +2 more sources

Numerical Solution of the Absolute Value Equations Using Two Matrix Splitting Fixed Point Iteration Methods

Journal of Function Spaces, 2022
The absolute value equations (AVEs) are significant nonlinear and non-differentiable problems that arise in the optimization community. In this article, we provide two new iteration methods for determining AVEs.
Rashid Ali, Asad Ali, Mohammad Mahtab Alam, Abdullah Mohamed   +3 more
doaj   +2 more sources

The Error and Perturbation Bounds of the General Absolute Value Equations

Journal of Optimization Theory and Applications
To our knowledge, the error and perturbation bounds of the general absolute value equations are not discussed. In order to fill in this study gap, in this paper, by introducing a class of absolute value functions, we study the error and perturbation bounds of two types of the general absolute value equations (AVEs): $Ax-B|x|=b$ and $Ax-|Bx|=b$.
Cui-Xia Li, Shi-Liang Wu
openaire   +3 more sources

Overdetermined Absolute Value Equations

, 2019
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.
Rohn, Jiří
openaire   +2 more sources

The new iteration methods for solving absolute value equations [PDF]

, 2023
summary:Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $ Ax-|x| = b$, where $A ...
Ali, Rashid, Pan, Kejia
core   +2 more sources

The modification of the generalized gauss-seidel iteration techniques for absolute value equations [PDF]

Computational Algorithms and Numerical Dimensions, 2022
This paper proposes two modified generalized Gauss-Seidel iteration techniques to determine the Absolute Value Equations (AVEs). Convergence of the new techniques is established under some appropriate conditions lastly; several numerical examples verify ...
Rashid Ali, Ashfaq Ahmad, Ijaz Ahmad, Asad Ali   +3 more
doaj   +1 more source

On the unique solvability and numerical study of absolute value equations

Journal of Numerical Analysis and Approximation Theory, 2019
The aim of this paper is twofold. Firstly, we consider the unique solvability of absolute value equations (AVE), \(Ax-B\vert x\vert =b\), when the condition \(\Vert A^{-1}\Vert
Achache Mohamed
doaj   +7 more sources