Usporedba egzaktnih i heurističkih metoda za numeričku aproksimaciju funkcija

master's thesis

• Title (english): Comparison of Exact and Heuristic Methods for Numerical Approximation of Functions
• Author: Mato Manović
• Mentor: Tomislav Burić (mentor)
• Committee member: Tomislav Burić (predsjednik povjerenstva)
• Committee member: Mario Krnić (član povjerenstva)
• Committee member: Lenka Mihoković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2019-07-11, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu su odabrane i implementirane neke od egzaktnih i heurističkih metoda koje su rješavale problem numeričke aproksimacije funkcija u obliku polinoma i racionalnih funkcija. U prvom dijelu rada su teorijski obrađene metode korištene u ovom radu uz osnove aritmetike na računalu za koje su aproksimacije namijenjene. U drugom dijelu rada su navedene aproksimacije na primjeru nekoliko elementarnih funkcija dobivene raznim metodama. Napravljena je usporedba aproksimacija zajedno s analizom prednosti i nedostataka egzaktnih metoda u odnosu na heurističke metode s obzirom na ponašanje funkcije unutar intervala za kojeg se računala aproksimacija.

Abstract (english)

This thesis deals with some of the exact and heuristic methods for solving numerical approximation of functions problem in terms of polynomial and rational functions. First part of thesis is concerned with theoretically analysing background of exact and heuristic methods used in the thesis along with computer arithmetic basis for which approximations are intended for. In the second part of the thesis there are mentioned approximations in the example of few elementary functions obtained by various methods. The results of comparison are presented together with analysis of pros and cons of exact methods in regard to heuristic methods considering function behaviour within interval for which approximation is calculated.

• Keywords: minimax aproksimacija; Čebiševljevi polinomi; Čebiševljev oscilatorni teorem; heuristički algoritmi; Padeova aproksimacija; računalna aritmetika; Maehlyeva metoda
• Keywords (english): minimax approximation; Chebyshev polynomials; Chebyshev equioscillation theorem; heuristic algorithms; Pade approximation; computer arithmetic; Maehly method
• Language: croatian
• URN:NBN: urn:nbn:hr:168:480190
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2020-01-07 20:00:22