Approximating a Zero of a Function via the Zero of Its 1/P Pade' Approximant

Author(s):

Dr. Abdel Wahab M. Nourein , Karary University

Keywords:

analytic; analytic function; zero; zero of a function; matrix; determinant; determinant of a matrix; Padé approximant; continuity; continuity of a function; iteration; iteration function; iteration formula

Abstract:

z* is said to be a zero of a function f(z) if f(z*) = 0. The problem of finding such a z* for given functions has raised due concern and received considerable attention. Numerous attempts have been put forward leading to quite a number of formulae. Nonetheless a lot more is sought and is still being considered. In this paper we give a simple – yet neat and elegant – procedure arising from approximating the function in question by its 1/p Pade’ approximant. The theme and essence of the method build on the zero of the 1/p Pade’ approximant – effectively on the zero of the linear expression in the numerator. This zero - provides the basis for a zero of the function in question - thus endorsing the beauty and neatness of the method.

Other Details:

Manuscript Id	:	IJSTEV7I12003
Published in	:	Volume : 7, Issue : 12
Publication Date	:	01/07/2021
Page(s)	:	33-35

Download Article