Open AccessAN ITERATIVE FORMULA FOR SIMULTANEOUS LOCATION OF THE ZEROS OF A POLYNOMIAL
Author(s) -
Dr.Abdel Wahab Nourein
Publication year - 2021
Publication title -
international journal of engineering applied science and technology
Language(s) - English
Resource type - Journals
ISSN - 2455-2143
DOI - 10.33564/ijeast.2021.v05i12.051
Subject(s) - taylor series , mathematics , polynomial , convergence (economics) , series (stratigraphy) , divided differences , rate of convergence , cubic function , mathematical analysis , computer science , key (lock) , paleontology , computer security , economics , biology , economic growth
Needless to say that the search for efficientalgorithms for determining zeros of polynomials has beencontinually raised in many applications. In this paper wegive a cubic iteration method for determiningsimultaneously all the zeros of a polynomial – assumeddistinct – starting with ‘reasonably close’ initialapproximations – also assumed distinct. The polynomial –in question – is expressed in its Taylor series expansion interms of the initial approximations and their correctionterms. A formula with cubic rate of convergence – basedon retaining terms up to 2ndorder of the expansion in thecorrection terms – is derived.