Antitrikotni (Batmanov) razcep za simetrične matrike

delo diplomskega seminarja

Samo Metličar (Author), Bor Plestenjak (Mentor)

Abstract

V delu obravnavamo antitrikotni razcep za simetrične nedefinitne matrike, znan tudi kot Batmanov razcep, katerega obstoj tudi dokažemo. Obravnavamo algoritem, ki z množenjem z ortogonalnimi matrikami pretvori vhodno matriko v bločno antitrikotno matriko, iz katere lažje razberemo inercijo in ocenimo lastne vrednosti. Omenjena dejstva so podprta tudi s primeri. V delo je vključena tudi analiza časovne zahtevnosti algoritma, ki lahko pri različnih vhodnih podatkih močno varira.

Keywords

matematika;Batmanov razcep;simetrične matrike;bločne antitrikotne matrike;lastne vrednosti;inercija;algoritmi;časovna zahtevnost;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[S. Metličar]
UDC:	519.6
COBISS:	18817881
Views:	1227
Downloads:	167
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Antitriagonal (Batman) decomposition for symmetric matrices
Secondary abstract:	In this work the antitriangular decomposition for symmetric matrices, also known as the Batman decomposition, is examined and it's existence is proved. An algorithm which uses the multiplication by orthogonal matrices to transform the input matrix to a block antitriangular matrix is presented. This algorithm allows us to determine the inertia and estimate the eigenvalues more efficiently. This claim is supported by examples. Also included in the work is the analysis of time complexity of the algorithm, which can variate strongly depending on the input data.
Secondary keywords:	Batman decomposition;symmetric matrices;block antitriangular matrices;eigenvalues;inertia;algorithms;time complexity;
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, Finančna matematika - 1. stopnja
Pages:	40 str.
ID:	11223596