Geometry and convergence of Euler's and Halley's methods

SIAM Review

Volumn 39, Issue 4, 1997, Pages 728-735

  Melman, A ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Euler's method; Global convergence; Halley's method

Indexed keywords

COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTERPOLATION; POLYNOMIALS; THEOREM PROVING;

EULER'S METHOD; HALLEY'S METHOD; TAYLOR POLYNOMIALS;

APPROXIMATION THEORY;

EID: 0031377365     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144595301140     Document Type: Article

References (13)

1. H. BATEMAN, Halley's method for solving equations, Amer. Math. Monthly, 45 (1938), pp. 11-17.
2. A. BEN-ISRAEL, Newton's method with modified function, Contemp. Math, 204 (1997), pp. 39-50.
3. G. H. BROWN, JR., On Halley's variation of Newton's method, Amer. Math. Monthly, 84 (1978), pp. 726-728.
4. W. GANDER, On Halley's iterntion method, Amer. Math. Monthly, 92 (1985), pp. 131-134.
5. E. HALLEY, Methodus nova, accurala & facihis inveniendi radices aequationum quarumcumqe generaliter, sine pracvia reductione, Philos. Trans. Roy. Soc. London, 18 (1694), pp. 136-148.
6. P. HENRICI, Elements of Numerical Analysis, John Wiley & Sons, Inc., New York, 1964.
7. A. M. OSTROWSKI, Solution of Equations in Euclidean and Banach Spaces, Acdemic Press, New York, 1973.
8. D. B. POPOVSKI, A family of one-point iterution formulae for finding roots, Internat. J. Comput. Math. Sect. B, 8 (1973), pp. 85-88.
9. G. S. SALEHOV, On the convergence of the process of tangent hyperbolas, Dokl. Akad. Nauk SSSR, 82 (1952), PP. 525-528 (in Russian).
10. R. A. SAFIEV, The method of tangent hyperbolas, Dokl. Akad. Nauk SSSR, 149 (1963), pp. 788-791 (in Russian). Translation in Soviet Math. Dokl., 4 (1963), pp. 482-485.
11. R. A. SAFIEV, The method of tangent hyperbolas, Dokl. Akad. Nauk SSSR, 149 (1963), pp. 788-791 (in Russian). Translation in Soviet Math. Dokl., 4 (1963), pp. 482-485.
12. T. R. SCAVO AND J. B. THOO, On the geometry of Halley's method, Amer. Math. Monthly, 102 (1995), pp. 417-426.
13. J. F. TRAUB, Iterative Methods for the Solutin of Equations, Prentice-Hall, Englewood Cliffis, NJ, 1964.