Finding polynomial roots using knot insertion

Rok Koleša (2014) Finding polynomial roots using knot insertion. EngD thesis.

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Abstract

In this thesis we present a new way of finding polynomial roots. First we find out what is interpolation, what are piecewise polynomials and what are B-splines. We write down the polynomial as a B-spline and then we use the close relation between the spline and it's control polygon by finding a root of the polygon, insert that root as a knot which we use as our first estimate and modify the polygon. The procedure is repeated until the estimates converge. We then proceed to find all the other roots by reseting all variables and start the whole procedure from the found root onwards. At the end we give a MATLAB implementation of the algorithm.

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