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master's thesis
B-splajn i interpolacija
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:937163
Šućur, Marija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Šućur, M. (2014). B-splajn i interpolacija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:937163

Šućur, Marija. "B-splajn i interpolacija." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:937163

Šućur, Marija. "B-splajn i interpolacija." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:937163

Šućur, M. (2014). 'B-splajn i interpolacija', Master's thesis, University of Zagreb, Faculty of Science, accessed 08 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:937163

Šućur M. B-splajn i interpolacija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 08] Available at: https://urn.nsk.hr/urn:nbn:hr:217:937163

M. Šućur, "B-splajn i interpolacija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:937163

Metadata
TitleB-splajn i interpolacija
AuthorMarija Šućur
MentorTina Bosner (mentor)
Committee memberTina Bosner (predsjednik povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberRobert Manger (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-11, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:937163
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-14 11:00:35