Fast and Stable Polynomial Root Finders - Part One

In general, Newton’s method for finding roots of polynomials is an effective and easy algorithm to both implement and use. However, certain weakness is exposed when trying to find roots in a polynomial with multiple roots. This paper highlights the weakness and devises a modification to the general Newton algorithm that can effectively cope with the multiple roots issue and deal with the usual pitfalls in using the Newton method to find polynomial roots. This paper is part of a multi-series of papers on how to use the same framework to implement different root finder methods.