B-splajn i interpolacija

master's thesis

• Author: Marija Šućur
• Mentor: Tina Bosner (mentor)
• Committee member: Tina Bosner (predsjednik povjerenstva)
• Committee member: Saša Singer (član povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog diplomskog rada je definirati B-splajn i pojasniti njegova svojstva. Započinjem definiranjem podijeljenih razlika i navođenjem njihovih osnovnih svojstava pomoću kojih će se pojasniti svojstva i definirati sam B-splajn nekog određenog reda. Zatim, pokazujem na koji način se jednostavno računaju B-splajnovi i zašto je izbor B-splajnova najpogodniji za interpolaciju funkcija. Kod interpolacije se spominje kolokacijska matrica B-splajnova koja ima jako zanimljiva svojstva: regularna je, totalno pozitivna i trakasta. Navedena svojstva olakšavaju postupak interpolacije. Pokazano je također da izborom točaka (Greville-ove točke) možemo smanjiti grešku interpolacije tako da se na samom kraju dobije gotovo najbolja moguća aproksimacija funkcije iz prostora splajnova.

Abstract (english)

The main goal of this thesis is to define B-spline and clarify its properties. It begins by defining the divided differences and mentioning their basic properties which will help to define B-spline and prove its properties. Then, it is shown how to easily calculate the B-spline and why is the choice of B-spline the most appropriate for function interpolation. In the fourth chapter was mentioned collocation matrix of B-splines that has very interesting properties. It is regular, total positive and banded. It was also shown that by good choice of points (Greville’s point) we can reduce the error of interpolation so that, at the end, we get almost the best possible approximation of functions from the spline space.

• Keywords: B-splajn; interpolacija funkcija; kolokacijska matrica B-splajnova
• Keywords (english): B-spline; function interpolation; collocation matrix of B-splines
• Language: croatian
• URN:NBN: urn:nbn:hr:217:499570
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-02-14 10:55:37