Geodesic
Maps for global separation of roots
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 241-256
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.
Classification : 65H05, 65H20, 65S05
Keywords: step function, fixed-point, iteration map, Newton map, halley map, sieve of eratosthenes 
@article{ETNA_2016__45__a13,
     author = {Gra\c{c}a,  M\'ario M.},
     title = {Maps for global separation of roots},
     journal = {Electronic transactions on numerical analysis},
     pages = {241--256},
     year = {2016},
     volume = {45},
     zbl = {1343.65053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a13/}
}
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JO  - Electronic transactions on numerical analysis
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%A Graça,  Mário M.
%T Maps for global separation of roots
%J Electronic transactions on numerical analysis
%D 2016
%P 241-256
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%F ETNA_2016__45__a13
Graça,  Mário M. Maps for global separation of roots. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 241-256. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a13/