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https://hdl.handle.net/20.500.11851/6723
Title: | Finiteness of the Area of Basins of Attraction of Relaxed Newton Method for Certain Holomorphic Functions | Authors: | Çilingir, Figen | Keywords: | relaxed Newton's method Newton business iteration of rational functions Julia set Fatou set |
Publisher: | World Scientific Publ Co Pte Ltd | Abstract: | For a nonconstant function F and a real number h is an element of] 0, 1] the relaxed Newton's method N-F,(h) of F is an iterative algorithm for finding the zeroes of F. We show that when relaxed Newton's method is applied to complex function F(z) = P(z)e(Q(z)), where P and Q are polynomials, the basin of attraction of a root of F has finite area if the degree of Q exceeds or equals 3. The key point is that N-F,(h) is a rational map with a parabolic fixed point at infinity. | URI: | https://doi.org/10.1142/S0218127404011879 https://hdl.handle.net/20.500.11851/6723 |
ISSN: | 0218-1274 |
Appears in Collections: | Matematik Bölümü / Department of Mathematics Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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