On the Guaranteed Convergence of the Japanese Zero-finding Method
Publications de l'Institut Mathématique, _N_S_73 (2003) no. 87, p. 59
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
One of the most important problems in solving nonlinear
equations is the construction of such initial conditions which provide
both the guaranteed and fast convergence of the considered numerical
method. Smale's approach from 1981, known as ``point estimation
theory", treats convergence conditions and the domain of convergence in
solving an equation $f(z)=0$ using only the information of $f$ at the
initial point $\boldsymbol{z}^{(0)}$. A procedure of this type is
applied in this paper to the fourth order iterative method for the
simultaneous approximation of simple zeros of polynomials, proposed by
Sakurai, Torii and Sugiura in 1991. We have stated initial conditions
which ensure the guaranteed convergence of this method. These
conditions are of significant practical importance since they are
computationally verifiable; they depend only on the coefficients of a
given polynomial, its degree $n$ and initial approximations to
polynomial zeros.
@article{10_2298_PIM0373059P,
author = {Miodrag S. Petkovi\'c and Lidija Ran\v{c}i\'c and Du\v{s}an Milo\v{s}evi\'c},
title = {On the {Guaranteed} {Convergence} of the {Japanese} {Zero-finding} {Method}},
journal = {Publications de l'Institut Math\'ematique},
pages = {59 },
publisher = {mathdoc},
volume = {_N_S_73},
number = {87},
year = {2003},
doi = {10.2298/PIM0373059P},
zbl = {1052.65043},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0373059P/}
}
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Miodrag S. Petković; Lidija Rančić; Dušan Milošević. On the Guaranteed Convergence of the Japanese Zero-finding Method. Publications de l'Institut Mathématique, _N_S_73 (2003) no. 87, p. 59 . doi: 10.2298/PIM0373059P
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