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Volumn 11, Issue 2, 2001, Pages 359-370

Julia sets for the super-Newton method, Cauchy's method, and Halley's method

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[No Author keywords available]

Indexed keywords


EID: 0035376969     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1368137     Document Type: Article
Times cited : (59)

References (21)
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  • 2
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    • Families of rational maps and iterative root-finding algorithms
    • C. McMullen, "Families of rational maps and iterative root-finding algorithms," Ann. Math. 125, 467-493 (1987).
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    • Newton's method and complex dynamical systems
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    • Haeseler, F.V.1    Peitgen, H.-O.2
  • 7
    • 38249043097 scopus 로고
    • On the existence of generally convergent algorithms
    • M. Shub and S. Smale, "On the existence of generally convergent algorithms," J. Complexity 2, 2-11 (1986).
    • (1986) J. Complexity , vol.2 , pp. 2-11
    • Shub, M.1    Smale, S.2
  • 8
    • 0003093795 scopus 로고
    • Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
    • E. Vrscay and W. Gilbert, "Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions," Numer. Math. 52, 1-16 (1988).
    • (1988) Numer. Math. , vol.52 , pp. 1-16
    • Vrscay, E.1    Gilbert, W.2
  • 9
    • 84966240099 scopus 로고
    • Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: A computer assisted study
    • E. Vrscay, "Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: A computer assisted study," Math. Comput. 46, 151-169 (1986).
    • (1986) Math. Comput. , vol.46 , pp. 151-169
    • Vrscay, E.1
  • 11
    • 0001050260 scopus 로고
    • Methodus nova. Accurata and facilis inveniendi radices Æquationum quarumcumque generaliter, sine prævia reductione
    • E. Halley, "Methodus Nova. Accurata and Facilis Inveniendi Radices Æquationum Quarumcumque Generaliter, Sine Prævia Reductione," Philos. Trans. R. Soc. London 18, 136-148 (1694).
    • (1694) Philos. Trans. R. Soc. London , vol.18 , pp. 136-148
    • Halley, E.1
  • 13
    • 0003275962 scopus 로고
    • A family of root finding methods
    • E. Hansen and M. Patrick, "A family of root finding methods," Numer. Math. 27, 257-269 (1977).
    • (1977) Numer. Math. , vol.27 , pp. 257-269
    • Hansen, E.1    Patrick, M.2
  • 14
    • 84958272496 scopus 로고    scopus 로고
    • Université Paul Sebatier, Toulouse, France, private communication
    • X. Buff, Université Paul Sebatier, Toulouse, France, private communication.
    • Buff, X.1
  • 16
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    • Random House Birkhäuser Mathematics Series, New York
    • R. P. Boas, Invitation to Complex Analysis (Random House Birkhäuser Mathematics Series, New York, 1987).
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    • Boas, R.P.1
  • 17
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    • Über unendlich viele algorithmen zur auflösung der gleichungen
    • E. Schröder, "Über unendlich viele Algorithmen zur Auflösung der Gleichungen," Math. Ann. 2, 317-364 (1870).
    • (1870) Math. Ann. , vol.2 , pp. 317-364
    • Schröder, E.1
  • 18
    • 84958272497 scopus 로고    scopus 로고
    • Newton's iteration method and its generalizations
    • to be published
    • W. Gilbert, "Newton's iteration method and its generalizations," Fractals (to be published).
    • Fractals
    • Gilbert, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.