Results 1 to 10 of about 7,772,771 (267)
The study of new fixed-point iteration schemes for solving absolute value equations [PDF]
HeliyonAbsolute value equations (AVEs) play a crucial role in solving various complexities across scientific computing, engineering, management science, and operations research.
Rashid Ali, Zhao Zhang, Fuad A. Awwad
doaj +2 more sources
A Newton-type technique for solving absolute value equations
Alexandria Engineering Journal, 2023 The Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson’s method. Convergence results are established under
Alamgir Khan +7 more
doaj +3 more sources
Modified Picard-like Method for Solving Absolute Value Equations
Mathematics, 2023 We present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of the absolute value equations as a two-by-two block nonlinear equation.
Yuan Liang, Chaoqian Li
doaj +2 more sources
Gauss Quadrature Method for System of Absolute Value Equations
Mathematics, 2023 In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step method in which the well-known Gauss quadrature rule is the corrector step and the generalized Newton method is taken as the predictor ...
Lei Shi +3 more
doaj +2 more sources
Preconditioned conjugate gradient methods for absolute value equations
Journal of Numerical Analysis and Approximation Theory, 2020 We investigate the NP-hard absolute value equations (AVE), \(Ax-B|x| =b\), where \(A,B\) are given symmetric matrices in \(\mathbb{R}^{n\times n}, \ b\in \mathbb{R}^{n}\).
Nassima Anane, Mohamed Achache
doaj +7 more sources
A New Efficient Method for Absolute Value Equations
Mathematics, 2023 In this paper, the two-step method is considered with the generalized Newton method as a predictor step. The three-point Newton–Cotes formula is taken as a corrector step. The proposed method’s convergence is discussed in detail.
Peng Guo +5 more
doaj +1 more source
Pre-Service Teachers’ Strategies in Solving Absolute Value Equations and Inequalities
Education Sciences, 2022 Many secondary school students have encountered difficulties when dealing with absolute value equations and inequalities. This condition might be brought to higher education, including by pre-service mathematics teachers in teacher training colleges. The
Al Jupri +2 more
doaj +1 more source
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 +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
The Picard-HSS-SOR iteration method for absolute value equations
Journal of Inequalities and Applications, 2020 In 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.
Lin Zheng
doaj +1 more source