20.500.12556/RUL-128454 Konstrukcija kubaturnih formul s pozitivnimi utežmi magistrsko delo Construction of cubature formulae with positive weights Delo obravnava pristope k numeričnem integriranju funkcij več spremenljivk. Opisani pristopi so uporaba kvadraturnih formul, reševanje sistema polinomskih enačb in verjetnostna metoda Monte Carlo. Glavni del naloge obravnava konstrukcijo formul s pozitivnimi utežmi. Izpeljane so meje za število vozlov teh formul in sistemi enačb, s katerimi dobimo vozle in uteži. Na koncu so navedeni primeri formul in analize njihovih napak. In the paper, some approaches to the numerical integration of multivariate functions are presented. Approaches that are considered include the use of quadrature formulae, solving a system of polynomial equations, and the probabilistic method Monte Carlo. The main part of the paper presents the construction of formulae with positive weights. Boundaries on the number of nodes of such formulae are derived and systems of equations that give us nodes and weights are presented. In the end examples of these formulae are given and their errors are examined. kubaturna formula numerična integracija pozitivna utež sistem polinomskih enačb cubature formula numerical integration positive weight system of polynomial equations true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2021-07-14 08:15:02 2021-07-14 08:15:08 2024-05-29 14:08:22 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 118161 69827587 2684.pdf 2684.pdf 1 64E236239E488AFF59E84B3501269D12 4902c3d80ac1259ca5bb2e2c9a7a984be27a790613b49a9d2eeb0b84a94a3ac6 b188d5ce-e46a-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=145196 Fakulteta za matematiko in fiziko 0 0 0