Razdaljne matrične napolnitve

delo diplomskega seminarja

Tadej Jeršin (Author), Aljaž Zalar (Mentor)

Abstract

V delu diplomskega seminarja obravnavamo problem razdaljnih matričnih napolnitev. Naš cilj je iz delno napolnjene matrike s podatki o razdaljah med točkami določiti vse razdalje oz. neznane elemente. Dokažemo zadosten pogoj za obstoj razdaljne matrične napolnitve in študiramo, kdaj je taka napolnitev enolična. Izpeljemo numeričen algoritem, ki ob izpolnjenem zadostnem pogoju vrne razdaljno matrično napolnitev. Predstavimo še problem iskanja razdaljnih matričnih napolnitev, kjer zadosten pogoj ni izpolnjen, vemo pa, da napolnitev obstaja.

Keywords

matrične napolnitve;razdaljne matrike;tetivni grafi;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[T. Jeršin]
UDC:	512
COBISS:	207598851
Views:	82
Downloads:	18
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Distance matrix completions
Secondary abstract:	In this thesis we adress the problem of distance matrix completions. The goal is to determine all distances or unknown elements in a partial matrix with data on the distances between points. We prove a sufficient condition for the existence of a distance matrix completion and derive conditions for its uniqueness. We present a numerical algorithm that returns a distance matrix completion when the sufficient condition is met. Additionally, we present the problem of finding a distance matrix completion where the sufficient condition is not met, but we know that a completion exists.
Secondary keywords:	matrix completions;distance matrices;chordal graphs;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	34 str.
ID:	24939871