ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65 Szabó, Zoltán István, Kossuth University, Debrecen, Hungary Root-finding Inclusion Algorithms Based on Tangential Lines and Parabolas For solving real non-linear equations of the form f(x) = 0, three iterative algorithms are given. They are based on Newton’s method and the always convergent method of tangential parabolas. Each of our combined procedures generates a decreasing sequence of real, compact intervals with a.) each member of the sequence contains the zero of the non-linear twice differentiable function f; b.) the sequence of diameters of the intervals tends to zero; c.) the diameters obey a quadratic à posteriori error estimation. In terms of error estimations, the parabola-parabola method is better than the other two combined algorithms. Some illustrative numerical examples are given, together with the algorithmic descriptions of our combined inclusion methods. Reference: Z. Szabó, Newton-Parabola Combined Method For Solving Equations, Comput. Appl. Math. I. Algorithms and Theory, pp.447-452. Elsevier Science Publishers,1992, IMACS.