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On the Convergence Ball and Error Analysis of the Modified Secant Method

Author

Listed:
  • Rongfei Lin
  • Qingbiao Wu
  • Minhong Chen
  • Xuemin Lei

Abstract

We aim to study the convergence properties of a modification of secant iteration methods. We present a new local convergence theorem for the modified secant method, where the derivative of the nonlinear operator satisfies Lipchitz condition. We introduce the convergence ball and error estimate of the modified secant method, respectively. For that, we use a technique based on Fibonacci series. At last, some numerical examples are given.

Suggested Citation

  • Rongfei Lin & Qingbiao Wu & Minhong Chen & Xuemin Lei, 2018. "On the Convergence Ball and Error Analysis of the Modified Secant Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:2704876
    DOI: 10.1155/2018/2704876
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    References listed on IDEAS

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    1. Ezquerro, J.A. & Hernández-Verón, M.A. & Velasco, A.I., 2015. "An analysis of the semilocal convergence for secant-like methods," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 883-892.
    2. Caliciotti, Andrea & Fasano, Giovanni & Roma, Massimo, 2018. "Preconditioned Nonlinear Conjugate Gradient methods based on a modified secant equation," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 196-214.
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