Asimptotski razvoji iterativnih sredina

master's thesis

• Title (english): Asymptotic Expansions of the Iterative Means
• Author: Stjepan Meštrović
• Mentor: Tomislav Burić (mentor)
• Committee member: Tomislav Burić (predsjednik povjerenstva)
• Committee member: Neven Elezović (član povjerenstva)
• Committee member: Ilko Brnetić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2017-02-20, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Cilj ovog diplomskog rada je analiza i implementacija teorije i algoritama iz područja vezanih uz aritmetičko-geometrijsku sredinu, sredine općenito te asimptotske razvoje. Aritmetičko-geometrijska sredina je vrijedna zbog svojih primjena u numeričkoj matematici (izračun konstanti od posebnog značaja u velikoj preciznosti, a malom broju iteracija). Dodatno su obrađene teorijska podloga sredina, veza sa eliptičkim integralima te konvergencija aritmetičko-geometrijske sredine. Kao drugi dio rada obrađena je teorija modernih istraživanja na temu složenih sredina, u tu svrhu definirani su asimptotski razvoji i operacije nad njima te teorija iterativnih postupaka.

Abstract (english)

The purpose of this Master's thesis is analysis and implementation of the theory and algorithms from the field of arithmetic-geometric mean, general means and asymptotic expansions. Arithmetic-geometric mean is valuable for its applications in numerical mathematics (computation of special constants in great precision, in small number of iterations). Furthermore, the theoretical background of means, connection with elliptic integrals and convergency of the arithmetic-geometric mean were studied. As a second part of this thesis the theory behind modern research on the topic of compound means is studied, asymptotic expansions and operations over them are defined and used to generate the coefficients of the compound means.

• Keywords: aritmetičko-geometrijska sredina; potencijske sredine; asimptotski razvoji
• Keywords (english): arithmetic-geometric mean; power means; asymptotic expansions
• Language: croatian
• URN:NBN: urn:nbn:hr:168:705891
• 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: 2019-03-13 22:59:13