Kvazi-interpolacija z B-zlepki

diplomsko delo

Luka Korotaj (Author), Tadej Kanduč (Mentor)

Abstract

V diplomskem delu se ukvarjamo s kvazi-interpolacijo. Pri klasični interpolaciji želimo potegniti krivuljo skozi vse podane točke, kar tipično privede do reševanja velikega sistema linearnih enačb, s kvazi-interpolacijo pa rešujemo več manjših, lokalnih sistemov. Pri kvazi-interpolaciji točk ne interpoliramo, temveč se jim dovolj dobro približamo. K nalogi pristopamo tako, da najprej pogledamo primer interpolacije s polinomi, potem pa definiramo in pojasnimo osnovne gradnike obravnavanih kvazi-interpolantov, to so t.i. B-zlepki. Zatem kvazi-interpolacijo formalno definiramo in dokažemo red konvergence za izbrane kvazi-interpolante. Tekom naloge izpeljane metode tudi implementiramo in jih prikažemo na grafih. Na koncu izpeljemo lokalno metodo najmanjših kvadratov in si pogledamo praktičen primer uporabe kvazi-interpolacije z odstranitvijo šuma iz signala.

Keywords

B-zlepki;aproksimacija;interpolacija; kvazi-interpolacija;računalništvo;matematika;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[L. Korotaj]
UDC:	004:51(043.2)
COBISS:	210057475
Views:	106
Downloads:	28
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Quasi-interpolation with B-splines
Secondary abstract:	In this thesis, we focus on quasi-interpolation. In classical interpolation, the goal is to draw a curve through all given points, which often results in a large system of linear equations. Quasi-interpolation, on the other hand, involves solving several smaller, local systems. With quasi-interpolation, we do not interpolate the points directly; instead, we approximate them sufficiently well. Our approach begins by examining an example of interpolation with polynomials, followed by the definition and explanation of the fundamental building blocks of quasi-interpolants, namely B-splines. We then formally define quasi-interpolation and prove the order of convergence for chosen quasi-interpolants. Throughout the thesis, we implement the derived methods and present them graphically. Finally, we derive the local method of least squares and explore a practical application of quasi-interpolation in noise removal from a signal.
Secondary keywords:	B-splines;approximation;interpolation;quasi-interpolation ;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:	1 spletni vir (1 datoteka PDF (36 str.))
ID:	24920784