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

Xiuhua Wang and Jisheng Kou ()
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Xiuhua Wang: Hubei Engineering University
Jisheng Kou: Hubei Engineering University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 3, No 13, 920-930

Abstract: 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.

Keywords: Nonlinear equations; Semilocal convergence; Chebyshev–Halley method; Recurrence relations (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0443-0

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