A family of Chebyshev-Halley type methods.

  1. Hernández, M.A. 1
  2. Salanova, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Aldizkaria:
International Journal of Computer Mathematics

ISSN: 0020-7160

Argitalpen urtea: 1993

Alea: 47

Zenbakia: 1-2

Orrialdeak: 59-63

Mota: Artikulua

SCOPUS: 2-s2.0-0002132387 WoS: WOS:A1993MR59600006 GOOGLE SCHOLAR

Beste argitalpen batzuk: International Journal of Computer Mathematics

Laburpena

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