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A New Newton Method with Memory for Solving Nonlinear Equations

Author

Listed:
  • Xiaofeng Wang

    (School of Mathematics and Physics, Bohai University, Jinzhou 121000, China)

  • Yuxi Tao

    (School of Mathematics and Physics, Bohai University, Jinzhou 121000, China)

Abstract

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.

Suggested Citation

  • Xiaofeng Wang & Yuxi Tao, 2020. "A New Newton Method with Memory for Solving Nonlinear Equations," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:108-:d:307186
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    References listed on IDEAS

    as
    1. Soleymani, F. & Lotfi, T. & Tavakoli, E. & Khaksar Haghani, F., 2015. "Several iterative methods with memory using self-accelerators," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 452-458.
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    Cited by:

    1. Ali Akgül & David Grow, 2023. "Fractal Newton Methods," Mathematics, MDPI, vol. 11(10), pages 1-13, May.

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