关于Halley迭代方法On Halley's Iteration Method
刘希普
摘要(Abstract):
用现代数学符号介绍了Halley迭代方法,给出了Halley迭代方法的代数解释,得到了一个关于三阶迭代的一般结果,指出许多有名的三阶迭代方法是这个结果的特殊情形。
关键词(KeyWords): 泰勒多项式;零点;迭代;修正
基金项目(Foundation):
作者(Author): 刘希普
DOI: 10.16393/j.cnki.37-1436/z.1997.02.010
参考文献(References):
- 1. G. Alefeld, On the convergence of Halley's method, this MoNTHLY, 1981; 88: 530-536
- 2. G. H. Brown, Jr., On Halley's variation of Newton's method, this MoNTHLY, 1977; 84: 726-728.
- 3. M. Davis and B. Dawson, On global convergence of Halley's iteration formula,Numer. Math., 1975;24: 133-135
- 4. H. Ehrmann, Konstruktion und Durchfuhrung von Iterationsverfahren hoherer Ordnung,Arch. Rational Mech. Anal., 1959; 4: 65-88
- 5. E. Hansen and M. Patrick, A family of root finding methods, Numer. Math., 1977; 27: 257-269.
- 6. E. Halley, Methodus Nova, Accurata & Facilis Inveniendi Radices Aequationum Quarumcumque Generaliter, Sine Praevia Reductione, Philos. Trans. Roy. Soc. London, 1694; 18: 136-148
- 7. P.Henrici, Elements of Numerical Analysis, Wiley, New York, 1964
- 8. __,Essentials of Numerical Analysis, Wiley, New York, 1982
- 9. __,Applied and Computational Complex Analysis, Wiley York, 1974.
- 10. A.M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, 1973
- 11. J. Stoer and R. Bulirsch, Intorduction to Numerical Analysis, Springer-Verlag, New York, 1980
- 12. J.F. Traub,Iterative Methods for Solution of Equations,Prentice-Hall, 1964