ISSN:
0945-3245
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Letf 0(x) be a function of one variable with a simple zero atr 0. An iteration scheme is said to be locally convergent if, for some initial approximationsx 1, ...,x s nearr 0 and all functionsf which are sufficiently close (in a certain sense) tof 0, the scheme generates a sequence {x k} which lies nearr 0 and converges to a zeror off. The order of convergence of the scheme is the infimum of the order of convergence of {x k} for all such functionsf. We study iteration schemes which are locally convergent and use only evaluations off,f′, ...,f [d] atx 1, ...,x k−1 to determinex k, and we show that no such scheme has order greater thand+2. This bound is the best possible, for it is attained by certain schemes based on polynomial interpolation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01402555
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