Volume 45, pp. 241-256, 2016.

Maps for global separation of roots

Mário M. Graça

Abstract

The global separation of the fixed-points of a real-valued function $g$ on an interval $D=[a,b]$ is considered by introducing the notions of quasi-step maps associated to $g$ and quasi-step maps educated by two predicates. The process of ‘education’ by the predicates is an a priori global technique which does not require initial guesses. The main properties of these maps are studied and the theoretical results are illustrated by some examples where appropriate quasi-step maps for Newton and Halley methods are applied.

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Key words

step function, fixed-point, iteration map, Newton map, Halley map, sieve of Eratosthenes

AMS subject classifications

65H05, 65H20, 65S05