A family of Chebyshev-Halley type methods.
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1
Universidad de La Rioja
info
ISSN: 0020-7160
Any de publicació: 1993
Volum: 47
Número: 1-2
Pàgines: 59-63
Tipus: Article
Altres publicacions en: International Journal of Computer Mathematics
Resum
The family under discussion comprises the iterative methods of the form x+:=x−[I+0.5Lf(x)(I−αLf(x))−1]f′(x)−1f(x) for solving nonlinear operator equations f(x)=0. Here, α∈[0,1] is the family parameter and Lf(x):=f′(x)−1f′′(x)f′(x)−1f(x). The authors carry out a Kantorovich-type convergence analysis for the methods of the family assuming that the second derivative f′′ satisfies the Lipschitz condition. The main theorem provides a convergence condition (independent of α), the uniqueness radius, and upper and lower error bounds. The performance of the methods is illustrated by three simple numerical examples