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Analysis of Convergence for Improved Chebyshev–Halley Methods Under Different Conditions

Author

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  • Xiuhua Wang

    (Hubei Engineering University)

  • Jisheng Kou

    (Hubei Engineering University)

Abstract

In this paper, we study a class of improved Chebyshev–Halley methods in Banach spaces and prove the semilocal convergence for these methods. Compared with the super-Halley method, these methods need one less inversion of an operator, and the R-order of these methods is also higher than the one of super-Halley method under the same conditions. Using recurrence relations, we analyze the semilocal convergence for these methods under two different convergence conditions. The convergence theorems are proved to show the existence and uniqueness of a solution. We also give some numerical results to show our approach.

Suggested Citation

  • Xiuhua Wang & Jisheng Kou, 2014. "Analysis of Convergence for Improved Chebyshev–Halley Methods Under Different Conditions," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 920-930, September.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:3:d:10.1007_s10957-013-0443-0
    DOI: 10.1007/s10957-013-0443-0
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