Primerjava asimptotskih metod za rodovne funkcije

diplomsko delo

Tomaž Poljanšek (Author), Matjaž Konvalinka (Mentor)

Abstract

Zaporedje lahko predstavimo z rodovno funkcijo, ki nam o zaporedju pove marsikaj. To nam še posebej pride prav, kadar nimamo enostavne eksplicitne formule zaporedja. Iz nekaterih lastnosti rodovne funkcije se da izpeljati asimptotske lastnosti koeficientov njenega zaporedja, kar lahko nato uporabimo za aproksimacijo koeficientov. V diplomski nalogi so predstavljene različne asimptotske metode. Te metode nato uporabimo na konkretnih rodovnih funkcijah, in sicer tako, da s temi metodami izračunamo asimptotske formule in med sabo primerjamo rezultate aproksimacije. Formule za določeno zaporedje so lahko pridobljene iz različnih metod in/ali imajo različno število členov. Izkaže se, da se asimptotske metode razlikujejo glede na enostavnost postopka in glede na natančnost aproksimacije.

Keywords

kombinatorika;asimptotika;rodovne funkcije;singularnosti;H-dopustnost;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2023
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[T. Poljanšek]
UDC:	51:004(043.2)
COBISS:	169062659
Views:	68
Downloads:	10
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Comparison of asymptotic methods for generating functions
Secondary abstract:	A sequence can be represented by a generating function, which tells us a lot about its sequence. This especially comes in useful when the sequence does not have a (simple) explitic formula. It is possible to derive sequence’s asymptotic characteristics of coefficients from its generating function, which can be used for the coefficients’ representation. In this diploma thesis we present some asymptotic methods. These are then used on some concrete generating functions in a way that we calculate asymptotic formulas with these methods and compare approximation results. Formulas can be derived by different methods and/or have different number of parts. It turns out that asymptotic methods differ in simplicity and approximation accuracy.
Secondary keywords:	combinatorics;asymptotics;generating functions;singularities;H-admissibility;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;
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:	45 str.
ID:	19937511