We study the relaxed Newton's method applied to polynomials. In particular, we give a technique such that for any n β₯ 2, we may construct a polynomial so that when the method is applied to a polynomial, the resulting rational function has an attracting cycle of period n. We show that when we use the
Convergence Criteria for Attracting Cycles of Newton's Method
β Scribed by Ocken, Stanley
- Book ID
- 118195196
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1998
- Tongue
- English
- Weight
- 706 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0036-1399
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π SIMILAR VOLUMES
The classical Kantorovich theorem on Newton's method assumes that the first 5 w Ε½ . derivative of the operator involved satisfies a Lipschitz condition β« FΠ x y 0 Ε½ .x5 5 5 FΠ y F L x y y . In this paper, we weaken this condition, assuming that 5 w Ε½ . Ε½ .x5 Ε½5 5 . β« FΠ x y FΠ x F x y x for a given
Let f(x) together with itsJirst two derivatives be continuous in the domain D and additionally let xlrl E D be an extremum (or turning point) of this function. Also, let x,, + , = T (x,, x,, \_ , , xn \_ J be Jarratt's Method for computing the extremum (or turning point) of a function. Criteria are