Iskanje ničel polinoma z vstavljanjem vozlov

diplomsko delo

Rok Koleša (Author), Gašper Jaklič (Mentor)

Abstract

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.

Keywords

polinom;ničla;interpolacija;vozel;B-zlepek;Matlab;poligon;računalništvo;računalništvo in informatika;univerzitetni študij;diplomske naloge;interdisciplinarni študij;

Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[R. Koleša]
UDC:	004.42:512.6(043.2)
COBISS:	1536144067
Views:	0
Downloads:	0
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Other data

Secondary language:	English
Secondary title:	Finding polynomial roots using knot insertion
Secondary 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.
Secondary keywords:	polynomial;root;interpolation;knot;B-spline;Matlab;polygon;computer science;computer and information science;diploma;interdisciplinary studies;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	47 str.
ID:	8739477