Dynamics of a family of third-order iterative methods that do not require using second derivatives

Applied Mathematics and Computation - Tập 154 Số 3 - Trang 735-746 - 2004
Sergio Amat1, Sonia Busquier1, Sergio Plaza2
1Departamento de Matemática Aplicada y Estadı́stica, Universidad Politécnica de Cartagena, Spain
2Depto. de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

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Tài liệu tham khảo

Arney, 1990, Exhibiting chaos and fractals with a microcomputer, Comput. Math. Appl., 19, 1, 10.1016/0898-1221(90)90037-K

Blanchard, 1984, Complex analytic dynamics on the Riemann sphere, Bull. AMS (new series), 11, 85, 10.1090/S0273-0979-1984-15240-6

Curry, 1983, On the iteration of a rational function: computer experiment with Newton method, Comm. Math. Phys., 91, 267, 10.1007/BF01211162

Drakopoulos, 1999, Generalized computation of Shröder iteration functions to motivated families of Julia and Mandelbrot-like sets, SIAM J. Numer. Anal., 36, 417, 10.1137/S0036142997317365

Drakopoulos, 1998, On the additional fixed points of Schröder iteration functions associated with a one-parameter family of cubic polynomials, Comput. Graph., 22, 629, 10.1016/S0097-8493(98)00071-5

Drakopoulos, 2002, Schröder iteration functions associated with a one-parameter family of biquedratic polynomials, Chaos, Solitons & Fractals, 13, 233, 10.1016/S0960-0779(00)00259-9

Emerenko, 1990, The dynamics of analytic transformations, Leningrad Math. J., 1, 563

Frontini, 2001, Some variants of Newton's method with third-order convergence, Quad. 474/P Dip. Mat. Politecnico di Milano

Ortega, 1970

1989

Potra, 1984

Vrscay, 1986, Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assisted study, Math. Comput., 46, 151

Vrscay, 1988, Extraneous fixed points, basin boundary and chaotic dynamics for Schröder and König rational iteration functions, Numer. Math., 52, 1, 10.1007/BF01401018

Weerakoom, 2000, A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett., 13, 87, 10.1016/S0893-9659(00)00100-2