Graphic and numerical comparison between iterative methods

Mathematical Intelligencer

Volumn 24, Issue 1, 2002, Pages 37-46

  Varona, Juan L ^a  

^a UNIVERSITY OF LA RIOJA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036003374     PISSN: 03436993     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03025310     Document Type: Article

References (21)

1. C. Alexander, I. Giblin, and D. Newton, Symmetry groups on fractals, The Mathematical Intelligencer 14 (1992), no. 2, 32-38.
2. I. K. Argyros, D. Chen, and Q. Qian, The Jarratt method in Banach space setting, J. Comput. Appl. Math. 51 (1994), 103-106.
3. I. K. Argyros and F. Szidarovszky, The Theory and Applications of Iteration Methods, CRC Press, Boca Raton, FL, 1993.
4. W. Bergweiler, Iteration of meromorphic functions, Bull. Am. Math, Soc. (N. S.) 29 (1993), 151-188.
5. P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Am. Math. Soc. (N. S.) 11 (1984), 85-141.
6. J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández, and M. A. Salanova, The application of an inverse-free Jarratt-type approximation to nonlinear Integral equations of Hammerstein-type, Comput. Math. Appl. 36 (1998), 9-20.
7. J. A. Ezquerro and M. A. Hernández, On a convex acceleration of Newton's method, J. Optim. Theory Appl. 100 (1999), 311-326.
8. W. Gander, On Halley's iteration method, Am. Math. Monthly 92 (1985), 131-134.
9. W. Gautschi, Numerical Analysis: An Introduction, Birkhäuser, Boston, 1997.
10. J. M. Gutiérrez and M. A. Hernández, A family of Chebyshev-Halley type methods in Banach spaces, Bull. Austral. Math. Soc. 55 (1997), 113-130.
11. M. A. Hernández, An acceleration procedure of the Whittaker method by means of convexity, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 20 (1990), 27-38.
12. P. Jarratt, Some fourth order multipoint Iterative methods for solving equations, Math. Comp. 20 (1966), 434-437.
13. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 2nd ed., Brooks/Cole, Pacific Grove, CA, 1996.
14. R. F. King, A family of fourth order methods for nonlinear equations, SIAM J. Numer. Anal. 10 (1973), 876-879.
15. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Monographs Textbooks Comput. Sci. Appl. Math., Academic Press, New York, 1970.
16. H. O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer-Verlag, New York, 1986.
17. M. Shub, Mysteries of mathematics and computation, The Mathematical Intelligencer 16 (1994), no. 2, 10-15.
18. J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.
19. W. Werner, Some improvements of classical iterative methods for the solution of nonlinear equations, in Numerical Solution of Nonlinear Equations (Proc., Bremen, 1980), E. L. Allgower, K. Glashoff and H. O. Peitgen, eds., Lecture Notes in Math. 878 (1981), 427-440.
20. S. Wolfram, The Mathematica Book, 3rd ed., Wolfram Media/Cambridge University Press, 1996.
21. J. W. Neuberger, The Mathematical Intelligencer, 21(1999), no. 3, 18-23.