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A New Newton Method with Memory for Solving Nonlinear Equations

School of Mathematics and Physics, Bohai University, Jinzhou 121000, China
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Mathematics 2020, 8(1), 108; https://doi.org/10.3390/math8010108
Received: 27 November 2019 / Revised: 24 December 2019 / Accepted: 29 December 2019 / Published: 10 January 2020
A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant parameter of Newton method without memory by a variable self-accelerating parameter, we obtain a novel Newton method with memory. The convergence order of the new Newton method with memory is 1 + 2 . The acceleration of the convergence rate is attained without any additional function evaluations. The main innovation is that the self-accelerating parameter is constructed by a simple way. Numerical experiments show the presented method has faster convergence speed than existing methods. View Full-Text
Keywords: simple roots; newton method; nonlinear equation; self-accelerating parameter; computational efficiency simple roots; newton method; nonlinear equation; self-accelerating parameter; computational efficiency
MDPI and ACS Style

Wang, X.; Tao, Y. A New Newton Method with Memory for Solving Nonlinear Equations. Mathematics 2020, 8, 108.

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