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On the Higher-Order Method for the Solution of a Nonlinear Scalar Equation

Author

Listed:
  • Min Chen

    (University of California)

  • Tsu-Shuan Chang

    (University of California)

Abstract

In this paper, a higher-order method for the solution of a nonlinear scalar equation is presented. It is proved that the new method is locally convergent with an order of (m+2), where m is the highest order derivative used in the iterative formula. Some numerical examples are used to demonstrate the new method.

Suggested Citation

  • Min Chen & Tsu-Shuan Chang, 2011. "On the Higher-Order Method for the Solution of a Nonlinear Scalar Equation," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 647-664, June.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:3:d:10.1007_s10957-011-9796-4
    DOI: 10.1007/s10957-011-9796-4
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    References listed on IDEAS

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    1. A. Germani & C. Manes & P. Palumbo & M. Sciandrone, 2006. "Higher-Order Method for the Solution of a Nonlinear Scalar Equation," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 347-364, December.
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    Cited by:

    1. Fazlollah Soleymani & Mahdi Sharifi & Bibi Somayeh Mousavi, 2012. "An Improvement of Ostrowski’s and King’s Techniques with Optimal Convergence Order Eight," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 225-236, April.
    2. Young Hee Geum & Young Ik Kim, 2014. "An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 608-622, February.

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    1. Fazlollah Soleymani & Mahdi Sharifi & Bibi Somayeh Mousavi, 2012. "An Improvement of Ostrowski’s and King’s Techniques with Optimal Convergence Order Eight," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 225-236, April.
    2. Young Hee Geum & Young Ik Kim, 2014. "An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 608-622, February.

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