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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A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems [PDF]
Journal of Mathematics, 2014 We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation.
Yuan Li, Hai-Shan Han, Dan-Dan Yang
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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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A Relaxation Iteration Method with Three Parameters for Solving Absolute Value Equation
Journal of Function SpacesIn this paper, a new matrix splitting iteration method is presented to solve the absolute value equation. The proposed method has three parameters, and it is expected that its convergence efficiency can be improved by selecting appropriate parameters ...
Lu-Lin Yan, Yi-Xin Jiang, Shu-Xin Miao
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A Two-Step Matrix-Splitting Iterative Method for Solving the Generalized Absolute Value Equation
Journal of MathematicsIn this paper, we present a two-step Newton-based matrix-splitting iteration method for solving the generalize absolute value equation. This method can produce a number of two-step Newton-based relaxation iteration algorithms with the right matrix ...
Lin Zheng, Yangxin Tang
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Generalized Perron Roots and Solvability of the Absolute Value Equation
SIAM Journal on Matrix Analysis and Applications, 2023 Let $A$ be a $n\times n$ real matrix. The piecewise linear equation system $z-A\vert z\vert =b$ is called an absolute value equation (AVE). It is well-known to be equivalent to the linear complementarity problem. Unique solvability of the AVE is known to be characterized in terms of a generalized Perron root called the sign-real spectral radius of $A$.
Manuel Radons, Josué Tonelli-Cueto
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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
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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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Sign controlled solvers for the absolute value equation with an application to support vector machines [PDF]
, 2017 Let A be a real n n matrix and z; b 2 Rn. The piecewise linear equation system z Ajzj = b is called an absolute value equation. It is equivalent to the general linear complementarity problem, and thus NP hard in general.
Lutz Lehmann +3 more
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Efficiency of Dynamic Computer Environment in Learning Absolute Value Equation [PDF]
, 2020 The presented study analyzes the usage of the didactic efficiency of multiple representations in a computer environment in learning absolute value functions and equations.
Marina Jokić, Đurdjica Takači
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