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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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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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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
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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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Linear Algebra and its Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mangasarian, O.L., Meyer, R.R.
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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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Interval algorithm for absolute value equations
Open Mathematics, 2011 Abstract We investigate the absolute value equations Ax−|x| = b. Based on ɛ-inflation, an interval verification method is proposed. Theoretic analysis and numerical results show that the new proposed method is effective.
Wang Aixiang, Wang Haijun, Deng Yongkun
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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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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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Residual Iterative Method for Solving Absolute Value Equations
Abstract and Applied Analysis, 2012 We suggest and analyze a residual iterative method for solving absolute value equations Ax-x=b where A∈Rn×n, b∈Rn are given and x∈Rn is unknown, using the projection technique. We also discuss the convergence of the proposed method.
Muhammad Aslam Noor +2 more
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