On Chebyshev-Halley methods with sixth-order convergence for solving non-linear equations. (English) Zbl 1122.65334

Kou, Jisheng

Appl. Math. Comput. 190, No. 1, 126-131 (2007).

Summary: We present a family of new variants of Chebyshev-Halley methods. The new methods have sixth-order convergence although they only add one evaluation of the function at the point iterated by Chebyshev-Halley methods. The numerical results presented show that the new methods work better not only in order but in efficiency.

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

Chebyshev-Halley methods; Newton’s method; non-linear equations; iterative method; root-finding; sixth-order convergence; numerical results

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