Konstrukcija kubaturnih formul s pozitivnimi utežmi : magistrsko delo

Naglič, Andraž (author), Žagar, Emil (mentor)

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.

• Language: Slovenian
• Keywords: kubaturna formula, numerična integracija, pozitivna utež, sistem polinomskih enačb
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-128454
• UDC: 519.6
• COBISS.SI-ID: 69827587
• Publication date in RUL: 14.07.2021

NAGLIČ, Andraž, 2021, Konstrukcija kubaturnih formul s pozitivnimi utežmi : magistrsko delo [online]. Master’s thesis. [Accessed 6 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=128454

Secondary language

• Language: English
• Title: Construction of cubature formulae with positive weights

Abstract

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.

• Keywords: cubature formula, numerical integration, positive weight, system of polynomial equations