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master's thesis
Kvazi Monte Carlo metoda za numeričku integraciju
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:724450
Turčić, Luka
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Turčić, L. (2018). Kvazi Monte Carlo metoda za numeričku integraciju (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:724450

Turčić, Luka. "Kvazi Monte Carlo metoda za numeričku integraciju." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:724450

Turčić, Luka. "Kvazi Monte Carlo metoda za numeričku integraciju." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:724450

Turčić, L. (2018). 'Kvazi Monte Carlo metoda za numeričku integraciju', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:724450

Turčić L. Kvazi Monte Carlo metoda za numeričku integraciju [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 June 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:724450

L. Turčić, "Kvazi Monte Carlo metoda za numeričku integraciju", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:724450

Metadata
TitleKvazi Monte Carlo metoda za numeričku integraciju
AuthorLuka Turčić
MentorVjekoslav Kovač (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
Committee memberRobert Manger (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Kvazi Monte Carlo metoda je determinističko poboljšanje Monte Carlo metode, vjerojatnosne metode koja se u rješavanju determinističkih problema oslanja na generiranje slučajnih uzoraka. Slučajni uzorci Monte Carlo metode su u kvazi Monte Carlo metodi zamijenjeni dobro odabranim determinističkim uzorcima, a idealan problem gdje se to može ilustrirati je problem numeričke integracije. Kriterij odabira determinističkih točaka je diskrepancija - kvantitativna mjera odstupanja od uniformne distribuiranosti niza. Glavni rezultati ovog rada dokazuju da je diskrepancija kriterij odabira točaka kvazi Monte Carlo metode, odnosno pokazuju da nizovi niske diskrepancije garantiraju manju grešku numeričke integracije. Potom rad daje neke konstrukcije takvih nizova, zajedno s dokazima da tako definirani nizovi jesu nizovi niske diskrepancije.
Abstract (english)
Quasi Monte Carlo method is a deterministic refinement of the Monte Carlo method, a probabilistic method which uses random samples for solving deterministic problems. Random samples from the Monte Carlo method are replaced with well-chosen deterministic samples and an ideal problem where this can be shown is the problem of numerical integration. The criterion for choosing deterministic points is discrepancy – a quantitative measure of deviation from the uniform distribution of a sequence. The main results of this thesis prove that discrepancy is the criterion for choosing quasi Monte Carlo samples, that is, they show that sequences of low discrepancy guarantee smaller error of numerical integration. Moreover, the thesis gives several constructions of such sequences with proofs that the constructed sequences are sequences of low discrepancy.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:724450
Study programmeTitle: Finance and Business Mathematics
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 on2019-07-02 12:03:11