LU-razcep matrik

diplomsko delo

Anja Jurgec (Author), Dušan Pagon (Mentor)

Abstract

V prvem delu diplomskega dela smo opisali Gaussovo eliminacijo kot algoritem za reševanje sistema linearnih enačb, s pomočjo katerega dobimo spodnje trikotno matriko L in zgornje trikotno matriko U oziroma LU-razcep. Sledi poglavje o uporabi trikotnega razcepa LU pri reševanju linearnih enačb s primeri: če poznamo trikotni razcep v LU, lahko sistem linearnih enačb rešimo v dveh korakih; determinanta matrike A, katere LU poznamo, je enaka determinanti matrike U; reševanje matričnih enačb; izračun inverzne matrike. Zaradi nepopolnosti uporabe Gaussove eliminacije sta opisana tudi delno in kompletno pivotiranje. Ker je trikotni razcep LU zelo uporaben, so v zadnjem delu predstavljeni nujni in zadostni pogoji za obstoj le-tega v primeru poljubne matrike.

Keywords

matematika;matrike;Gaussova eliminacija;razcepi;linearna algebra;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2009
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[A. Jurgec]
UDC:	51(043.2)
COBISS:	17178632
Views:	6164
Downloads:	786
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	LU DECOMPOSITION OF MATRICES
Secondary abstract:	In the first part of graduation thesis we describe Gauss elimination as an algorithm for solving a system of linear equations and with which we obtain lower triangular matrix L and upper triangular matrix U or LU decomposition. In a following chapter we consider diferent options of using LU decomposition when solving linear equations with the following examples: when knowing LU decomposition a system of linear equations is solvable in two steps; the determinant of a matrix A, for which a LU decomposition is known, equals the determinant of the matrix U; solving equations with matrices; calculating inverse matrix. Because of Gauss elimination's deficient use we also present full and partial pivoting. Since knowing LU decomposition of a matrix is really useful in the last part we give necessary and sucient conditons for its existence.
Secondary keywords:	matrices;linear equations;LU decomposition;Gauss elimination;pivoting;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 40 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18085