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The Convergence Ball and Error Analysis of the Relaxed Secant Method

Author

Listed:
  • Rongfei Lin
  • Qingbiao Wu
  • Minhong Chen
  • Lu Liu

Abstract

A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given.

Suggested Citation

  • Rongfei Lin & Qingbiao Wu & Minhong Chen & Lu Liu, 2017. "The Convergence Ball and Error Analysis of the Relaxed Secant Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:6976205
    DOI: 10.1155/2017/6976205
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    References listed on IDEAS

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    1. Argyros, Ioannis K. & Cordero, Alicia & Magreñán, Alberto & Torregrosa, Juan R., 2015. "On the convergence of a damped Newton-like method with modified right hand side vector," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 927-936.
    2. Argyros, Ioannis K. & George, Santhosh, 2016. "Unified convergence domains of Newton-like methods for solving operator equations," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 106-114.
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