Amat, S.; Bermúdez, C.; Busquier, S.; Leauthier, P.; Plaza, S. On the dynamics of some Newton’s type iterative functions. (English) Zbl 1165.65341 Int. J. Comput. Math. 86, No. 4, 631-639 (2009). Summary: The dynamics of a family of Newton’s type iterative methods for second- and third-degree complex polynomials is studied. The conjugacy classes of these methods are presented. Classical properties of rational maps are used. Cited in 1 ReviewCited in 2 Documents MSC: 65H05 Numerical computation of solutions to single equations 65E05 General theory of numerical methods in complex analysis (potential theory, etc.) 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 37N30 Dynamical systems in numerical analysis Keywords:iterative methods; dynamics; rational maps; conjugacy classes; nonlinear equations; Newton method; complex polynomials PDFBibTeX XMLCite \textit{S. Amat} et al., Int. J. Comput. Math. 86, No. 4, 631--639 (2009; Zbl 1165.65341) Full Text: DOI Link Link References: [1] DOI: 10.1016/S0096-3003(03)00747-1 · Zbl 1057.65023 · doi:10.1016/S0096-3003(03)00747-1 [2] DOI: 10.1007/s00010-004-2733-y · Zbl 1068.30019 · doi:10.1007/s00010-004-2733-y [3] DOI: 10.1017/S1446181100003539 · Zbl 1130.37043 · doi:10.1017/S1446181100003539 [4] DOI: 10.1016/0898-1221(90)90037-K · Zbl 0728.68131 · doi:10.1016/0898-1221(90)90037-K [5] Barna B., Publ. Math. Debrecen 4 pp 384– (1956) [6] Beardon A. F., Graduate Texts Mathematics 132 (1991) [7] DOI: 10.1090/S0273-0979-1984-15240-6 · Zbl 0558.58017 · doi:10.1090/S0273-0979-1984-15240-6 [8] Blanchard P., Fractal Geometry and Analysis pp 45– (1991) [9] DOI: 10.1088/0951-7715/16/3/312 · Zbl 1030.37030 · doi:10.1088/0951-7715/16/3/312 [10] DOI: 10.2307/2369201 · JFM 11.0260.02 · doi:10.2307/2369201 [11] Cayley A., Proc. Cambridge Philes. Soc. 3 pp 231– (1983) [12] Cosnard M., C.R. Acad. Sci. 297 pp 549– [13] DOI: 10.1007/BF01211162 · Zbl 0524.65032 · doi:10.1007/BF01211162 [14] Emerenko A., Leningrad Math. J 1 pp 563– (1990) [15] DOI: 10.1080/00207169608804539 · Zbl 0871.65038 · doi:10.1080/00207169608804539 [16] DOI: 10.1080/00207169408804280 · Zbl 0824.65025 · doi:10.1080/00207169408804280 [17] Hurley M., Trans. AMS 237 pp 143– (1986) [18] C. McMullen,Complex Dynamics and Renormalization. Annals of Mathematics Studies, Princeton University Press, 1994 · Zbl 0822.30002 [19] J. Milnor,Dynamics in one complex dimension: introductory lectures, preprint #1990/5 (1990), SUNY StonyBrook, Institute for Mathematical Sciences · Zbl 0946.30013 [20] Milnor J., Dynamics in One Complex Variable Introductory Lectures (1999) · Zbl 0946.30013 [21] Morosawa S., Holomorphic Dynamics (1999) [22] Peitgen H. O., Newton’s Method and Dynamical Systems (1989) · Zbl 0669.00021 · doi:10.1007/978-94-009-2281-5 [23] DOI: 10.4067/S0716-09172001000100001 · doi:10.4067/S0716-09172001000100001 [24] DOI: 10.1142/S0218127404011399 · Zbl 1129.37332 · doi:10.1142/S0218127404011399 [25] N. Steinmetz,Rational Iteration. de Gruyter Studies in Mathematics, Vol. 16, Walter de Gruyter, 1993 · Zbl 0773.58010 [26] DOI: 10.1007/BF03025310 · Zbl 1003.65046 · doi:10.1007/BF03025310 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.