Newtons Methode

ZIE OOK: Alfa-test, benaderen van nul, vast punt, irrationele formule van Halley, methode van Halley, methode van Horner, methode van Householder, methode van Laguerre, iteratie van Newton, vectorveld van Newton, algoritme voor het vinden van wortels

Abramowitz, M. en Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9e druk. New York: Dover, p. 18, 1972.

Acton, F. S. Ch. 2 in NumericalMethods That Work. Washington, DC: Math. Assoc. Amer., 1990.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 963-964, 1985.

Boyer, C. B. and Merzbacher, U. C. AHistory of Mathematics, 2nd ed. New York: Wiley, 1991.

Dickau, R. M. “Aantrekkingsbekkens voor Using Newton’s Method in the Complex Plane.” https://mathforum.org/advanced/robertd/newtons.html.

Dickau, R. M. “Variaties op de Methode van Newton.” https://mathforum.org/advanced/robertd/newnewton.html.

Dickau, R. M. “Compilatie van Iteratieve en Lijstbewerkingen.” MathematicaJ. 7, 14-15, 1997.

Gleick, J. Chaos: Making a New Science. New York: Penguin Books, plaat 6 (na p. 114) en p. 220, 1988.

Gourdon, X. en Sebah, P. “Newton’s Iteration.” https://numbers.computation.free.fr/Constants/Algorithms/newton.html.

Householder, A. S. Principlesof Numerical Analysis. New York: McGraw-Hill, pp. 135-138, 1953.

Mandelbrot, B. B. TheFractal Geometry of Nature. San Francisco, CA: W. H. Freeman, 1983.

Newton, I. Methodus fluxionum et serierum infinitarum. 1664-1671.

Ortega, J. M. and Rheinboldt, W. C. Iterative Solution of Nonlinear Equations in Several Variables. Philadelphia, PA: SIAM, 2000.

Peitgen, H.-O. and Saupe, D. TheScience of Fractal Images. New York: Springer-Verlag, 1988.

Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; and Vetterling, W.T. “Newton-Raphson Method Using Derivatives” en “Newton-Raphson Methods for Nonlinear Systems of Equations.” §9.4 en 9.6 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, Engeland: Cambridge University Press, pp. 355-362 en 372-375, 1992.

Ralston, A. and Rabinowitz, P. §8.4 in AFirst Course in Numerical Analysis, 2nd ed. New York: McGraw-Hill, 1978.

Raphson, J. Analysis aequationum universalis. Londen, 1690.

Smale, S. “On the Efficiency of Algorithms of Analysis.” Bull. Amer.Math. Soc. 13, 87-121, 1985.

Varona, J. L. “Graphic and Numerical Comparison Between Iterative Methods. “Math. Intell. 24, 37-46, 2002.

Whittaker, E. T. and Robinson, G. “The Newton-Raphson Method.” §44 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 84-87, 1967.