dc.contributor.author Gutierrez, J. M. dc.contributor.author Hernandez, L. J. dc.contributor.author Magreñán, Á. Alberto dc.contributor.author Rivas, M. T. dc.date 2016 dc.date.accessioned 2020-05-11T11:04:10Z dc.date.available 2020-05-11T11:04:10Z dc.identifier.isbn 9783319392288 dc.identifier.issn 2199-3041 dc.identifier.uri https://reunir.unir.net/handle/123456789/10036 dc.description.abstract The relaxed Newton's method modifies the classical Newton's method with a parameter h in such a way that when it is applied to a polynomial with multiple roots and we take as parameter one of these multiplicities, it is increased the order of convergence to the related multiple root. es_ES For polynomials of degree three or higher, the relaxed Newton's method may possess extraneous attracting (even super-attracting) cycles. The existence of such cycles is an obstacle for using the relaxed Newton's method to find the roots of the polynomial. Actually, the basins of these attracting cycles are open subsets of C. The authors have developed some algorithms and implementations that allow to compute the measure (area or probability) of the basin of a p-cycle when it is taken in the Riemann sphere. In this work, given a non negative integer n, we use our implementations to study the basins of non-repelling p-cycles, for 1 <= p <= n, when we perturb the relaxing parameter h. As a consequence, we quantify the efficiency of the relaxed Newton's method by computing, up to a given precision, the measure of the different attracting basins of non-repelling cycles. In this way, we can compare the measure of the basins of the ordinary fixed points (corresponding to the polynomial roots) with the measure of the basins of the point at infinity and the basins of other non-repelling p-cyclic points for p > 1. dc.language.iso eng es_ES dc.publisher Advances in iterative methods for nonlinear equations es_ES dc.relation.ispartofseries ;vol. 10 dc.relation.uri https://link.springer.com/chapter/10.1007%2F978-3-319-39228-8_9 es_ES dc.rights restrictedAccess es_ES dc.subject simple root es_ES dc.subject parameter plane es_ES dc.subject riemann sphere es_ES dc.subject double root es_ES dc.subject spherical triangle es_ES dc.subject WOS(2) es_ES dc.subject Scopus(2) es_ES dc.title Measures of the Basins of Attracting n-Cycles for the Relaxed Newton's Method es_ES dc.type bookPart es_ES reunir.tag ~ARI es_ES dc.identifier.doi https://doi.org/10.1007/978-3-319-39228-8_9
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