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dc.contributor.authorNorthshield, Sam
dc.date.accessioned2018-04-09T18:23:10Z
dc.date.accessioned2020-06-22T14:35:31Z
dc.date.available2018-04-09T18:23:10Z
dc.date.available2020-06-22T14:35:31Z
dc.date.issued1997
dc.identifier.citationNorthshield, S. (1997). On Iterates of Moebius transformations on fields. Mathematics of Computation, http://doi.org/10.1090/S0025-5718-00-01242-4en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12648/1123
dc.descriptionThis article has been published in the October 1997 issue of Mathematics of Computation.en_US
dc.description.abstractLet p be a quadratic polynomial over a splitting field K, and S be the set of zeros of p. We define an associative and commutative binary relation on G ≡ K ∪ {∞ } -S so that every Moebius transformation with fixed point set S is of the form x plus" c for some c. This permits an easy proof of Aitken acceleration as well as generalizations of known results concerning Newton's method, the secant method, Halley's method, and higher order methods. If K is equipped with a norm, then we give necessary and sufficient conditions for the iterates of a Moebius transformation m to converge (necessarily to one of its fixed points) in the norm topology. Finally, we show that if the fixed points of m are distinct and the iterates of m converge, then Newton's method converges with order 2, and higher order generalizations converge accordingly.en_US
dc.languageen_USen_US
dc.language.isoen_USen_US
dc.publisherMathematics of Computationen_US
dc.titleOn Iterates of Moebius transformations on fieldsen_US
dc.typeArticleen_US
refterms.dateFOA2020-06-22T14:35:31Z
dc.description.institutionSUNY Plattsburgh


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