projektna naloga
Gorazd Švelc (Author), Matej Mencinger (Mentor)

Abstract

Cilj te diplomske naloge je izdelava aproksimacijskega algoritma na podlagi teoretičnega ozadja polinomske aproksimacije funkcij ene spremenljivke. V sklopu algoritma delo obravnava posebno družino polinomov, ki definirajo interpolacijske točke, katere se asimptotično zgostijo proti začetku in na koncu intervala in s tem bistveno izboljšajo aproksimacijo. Delo povzema še konstrukcijo Newtonovega polinoma deljenih diferenc in njegovo vlogo pri polinomskih aproksimacijah funkcij, ter podaja nekaj primerov različnih interpolacijskih pristopov k aproksimaciji funkcij. To diplomsko delo vsebuje tudi izvorno kodo programa v programskem jeziku TI Basic, ki je avtorjevo izvirno delo.

Keywords

algoritmi;aproksimacijski algoritmi;polinomi;aproksimacija;interpolacija;izračun verižnice;deljene diference;polinomi Čebišova;TI Basic;TI Nspire CAS;matematika;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UM FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
Publisher: [G. Švelc]
UDC: 517.518.8
COBISS: 18733846 Link will open in a new window
Views: 1705
Downloads: 158
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Other data

Secondary language: English
Secondary title: Polynomial approximation of one-variable functions by Newton's divided difference polynomial and Chebyshev interpolation nodes on TI Nspire CAS calculators.
Secondary abstract: This diploma work aims to construct the approximation algorithm based on theory of polynomial approximation of arbitrary one-variable functions. It presents a group of polynomials that defines interpolation nodes with asymptotic accumulation towards the edges, for which maximum approximation error is guaranteed to diminish with increasing polynomial order. This document summarizes the construction of Newton’s divided differences polynomial and presents several cases of approximation with different interpolation methods. It also provides an original source code of the program, written in TI Basic programming language.
Secondary keywords: approximation;interpolation;divided differences;Chebyshev polynomials;TI Basic;TI Nspire CAS;
URN: URN:SI:UM:
Type (COBISS): Diploma project paper
Thesis comment: Univ. v Mariboru, Fak. za gradbeništvo
Pages: VI, 7-42 f.
ID: 8726898