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

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  • 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, Hindawi, vol. 2018, pages 1-5, July.
    • Handle: RePEc:hin:jnlamp:2704876
    DOI: 10.1155/2018/2704876
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