Newton's method is one of the important algorithms for solving absolute value equations. In this paper, we introduce an efficient two-step iterative method to improve the Newton algorithm. The new method adopts the predictor-corrector technique in which the first step is generalized Newton method and the second step is based on Simpson's $3/8$ rule. Under some standard assumptions, the convergence of new method and its linear convergence rate are obtained. Numerical results show that the our method is efficient and robust to solve absolute value equations.
Rahpeymaii, F. and Rostami, M. (2025). An iterative method based on Simpson's $3/8$ rule to solve absolute value equations. Journal of Mathematical Modeling, 13(3), 553-562. doi: 10.22124/jmm.2025.28919.2572
MLA
Rahpeymaii, F. , and Rostami, M. . "An iterative method based on Simpson's $3/8$ rule to solve absolute value equations", Journal of Mathematical Modeling, 13, 3, 2025, 553-562. doi: 10.22124/jmm.2025.28919.2572
HARVARD
Rahpeymaii, F., Rostami, M. (2025). 'An iterative method based on Simpson's $3/8$ rule to solve absolute value equations', Journal of Mathematical Modeling, 13(3), pp. 553-562. doi: 10.22124/jmm.2025.28919.2572
CHICAGO
F. Rahpeymaii and M. Rostami, "An iterative method based on Simpson's $3/8$ rule to solve absolute value equations," Journal of Mathematical Modeling, 13 3 (2025): 553-562, doi: 10.22124/jmm.2025.28919.2572
VANCOUVER
Rahpeymaii, F., Rostami, M. An iterative method based on Simpson's $3/8$ rule to solve absolute value equations. Journal of Mathematical Modeling, 2025; 13(3): 553-562. doi: 10.22124/jmm.2025.28919.2572
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