Please use this identifier to cite or link to this item: 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
Issue Date: 2004
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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