Iskanje ničel polinoma z vstavljanjem vozlov

Koleša, Rok (author), Jaklič, Gašper (mentor)

V tem diplomskem delu opišemo nov način iskanja ničel polinoma. Najprej spoznamo interpolacijo, odsekoma polinomske funkcije in B-zlepke. Polinom predstavimo v obliki B-zlepka, potem pa izkoristimo tesno povezanost polinoma z njegovim kontrolnim poligonom. Glavna ideja je, da poiščemo neko ničlo poligona, kar nam služi kot prvi približek, jo vstavimo med vozle in modificiramo celoten poligon. Postopek ponavljamo, dokler približki ne konvergirajo. Vse ničle dobimo tako, da najprej poiščemo prvo ničlo, počistimo vse približke, ponastavimo vse spremenljivke in celoten postopek ponovimo od tiste točke naprej. Podana je tudi MATLAB implementacija algoritma.

• Language: Slovenian
• Keywords: polinom, ničla, interpolacija, vozel, B-zlepek, MATLAB, poligon
• Work type: Bachelor thesis/paper
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2014
• PID: 20.500.12556/RUL-29566
• Publication date in RUL: 24.09.2014

Secondary language

• Language: English
• Title: Finding polynomial roots using knot insertion

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.

• Keywords: polynomial, root, interpolation, knot, B-spline, MATLAB, polygon