Newton's Iteration Method and its Generalizations

William J. Gilbert

References

  1. P. Blanchard, Complex Analytic Dynamics on the Riemann Sphere, Bull. Amer. Math. Soc. 11(1984), 85-141.
  2. L. Collatz, Functional Analysis and Numerical Mathematics, Academic Press, New York, 1966.
  3. J. Curry, L. Garnett, and D. Sullivan, On the iteration of rational functions: computer experiments with Newton's method, Commun. Math. Phys., 91 (1983), 267-277.
  4. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, Redwood City, Calif., 1989.
  5. A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup., 18 (1985), 287-343.
  6. F. v. Haeseler and H.-O. Peitgen, Newton's Method and Complex Dynamical Systems. Acta Appl. Math. 13 (1988), 3-58; also in Newton's Method and Dynamical Systems, edited by H.-O. Peitgen, Kluwer, Dordrecht, 1989.
  7. P. Henrici, Elements of Numerical Analysis, Wiley, New York, 1964.
  8. A. S. Householder, Principles of Numerical Analysis, Dover, New York, 1974.
  9. L. Keen, Julia Sets, in Proceedings of Symposia in Applied Mathematics, Vol. 39, Chaos and Fractals, edited by R. L. Devaney and L. Keen, American Math. Society, Providence, Rhode Island, 1989, 57-74.
  10. C. McMullen, Families of rational maps and iterative root-finding algorithms, Ann. Math. 125 (1987), 467-493.
  11. H.-O. Peitgen, D. Saupe, and F. v. Haeseler, Cayley's Problem and Julia Sets, Mathematical Intelligencer 6 (1984), 11-20.
  12. K. Sato, Global convergence features of Newton's method applied to polynomial equations, in Lecture Notes in Numerical and Applied Analysis, Vol. 3, The Newton Method and Related Topics, edited by H. Fujita and M. Yamaguti, Kinokuniya, Tokyo, 1981, 23-56.
  13. E. R. Vrscay, Julia Sets and Mandelbrot-Like Sets associated with Higher Order Schröder Rational Iteration Functions: A Computer Assisted Study, Math. Comp., 46 (1986), 151-169.
  14. E. R. Vrscay and W. J. Gilbert, Extraneous Fixed Points, Basin Boundaries and Chaotic Dynamics for Schröder and König Rational Iteration Functions, Numer. Math. 52 (1988), 1-16.
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