Računanje realnih ničel funkcij z uporabo Čebiševih polinomov

diplomsko delo

Blaž Oven (Author), Marjetka Krajnc (Mentor)

Abstract

V diplomskem delu bomo predstavili Čebiševe polinome prve in druge vrste, njihove lastnosti ter Čebiševo vrsto. Uporabili bomo Čebiševe polinome prve vrste za iskanje ničel gladke funkcije f na danem intervalu. Najprej bomo funkcijo aproksimirali z Čebiševimi polinomi in nato nad končno Čebiševo vrsto uporabili polinomske iskalnike ničel. V nadaljevanju pa bomo predstavili, kako najti ničle polinomske funkcije na nekem intervalu, ki ga bomo pri nekaterih algoritmih razdelili na podintervale z namenom natančnejšega in tudi hitrejšega iskanja ničel. Predstavljenih bo nekaj algoritmov in njihova uporaba, pa tudi njihove zahtevnosti, slabosti in omejitve. V okviru dela smo algoritme tudi sprogramirali v programu Matlab. Njihova praktična uporaba bo predstavljena na primerih.

Keywords

ničle;Čebiševi polinomi;Čebiševa vrsta;pretvorba v potence;podvajanje stopnje;računalništvo;računalništvo in informatika;računalništvo in matematika;univerzitetni študij;diplomske naloge;interdisciplinarni študij;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[B. Oven]
UDC:	517.518.8:004:4(043.2)
COBISS:	1536776899
Views:	96
Downloads:	4
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Calculating real roots using Chebyshev polynomials
Secondary abstract:	In this work, Chebyshev polynomials of the first and the second kind, their properties and the Chebyshev series will be examined. We will use Chebyshev polynomials of the first kind to find roots of the smooth function f on the given interval. At first the function will be approximated and then the polynomial root-finders on the truncated Chebyshev series will be used. In the next chapter we will study how to find roots of a polynomial function on the interval which we will, with some algorithms, divide on subintervals with the purpose of more accurate and faster finding of the roots. Different algorithms and their use, their complexity and their strengths and weaknesses will be presented. During this work we have also programmed these algorithms in Matlab. We will show their practical application on some examples.
Secondary keywords:	roots;Chebyshev polynomials;Chebyshev series;convert to powers;degree doubling;computer science;computer and information science;computer science and mathematics;diploma;interdisciplinary studies;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	47 str.
ID:	9123744