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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
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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
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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
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On the solution of general absolute value equations
Applied Mathematics Letters, 2020 In this note, we provide necessary and sufficient conditions that ensure the existence and uniqueness of solution of the general form of absolute value equations (AVEs), A x − B | x | = b .
Francesco Mezzadri
exaly +2 more sources
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 +3 more
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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
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Interval algorithm for absolute value equations
Open Mathematics, 2011 Wang Aixiang, Wang Haijun, Deng Yongkun
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Properties of the solution set of absolute value equations and the related matrix classes [PDF]
SIAM Journal on Matrix Analysis and Applications, 2022 The absolute value equations (AVE) problem is an algebraic problem of solving Ax+|x|=b. So far, most of the research focused on methods for solving AVEs, but we address the problem itself by analysing properties of AVE and the corresponding solution set.
Milan Hladík
semanticscholar +1 more source
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
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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
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