CONDITION NUMBERS OF THE STEFFENSEN’S ACCELERATION

K. Belghaba (Algeria) and M. N. Senhadji (Algeria)

Received August 14, 2006

References:

[1] A. C. Aitken, On Bernoulli’s numerical solution of algebraic equations, Proc. Roy. Soc. Edinburgh 46 (1926), 289-305. [2] A. C. Aitken, Studies in practical mathematics, II, Proc. Roy. Soc. Edinburgh 57 (1937), 239-304. [3] C. Brezinski, Accélération de la convergence en analyse numérique, Lecture Notes in Mathematics, Vol. 584, Springer, Berlin, 1977. [4] C. Brezinski and M. Redvo-Zaglia, Extrapolation Methods. Theory and Practice, North-Holland, Amsterdam, 1991. [5] E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. [6] M. N. Senhadji, On condition numbers of some quasi-linear transformations, J. Comput. Appl. Math. 104(1) (1999), 1-17. [7] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd ed., Springer-Verlag, Berlin, 1991. [8] P. Wynn, On a device for computing the transformation, Math. Tables Aids Comput. 10 (1956), 91-96.

Keywords and phrases: Aitken’s process, fixed-point, condition, Steffensen’s method.