On The Difference Of The Number Of Zeros And Poles Of The Members Of Convergent Sequences Of Meromorphic Functions
In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that...
For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.