20.500.12556/DKUM-11770 LU-RAZCEP MATRIK LU DECOMPOSITION OF MATRICES V prvem delu diplomskega dela smo opisali Gaussovo eliminacijo kot algoritem za reševanje sistema lineranih enačb, s pomočjo katerega pridobimo 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 razcepv 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. 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 different 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 sufficient conditons for its existence. matrike linearne enačbe LU-razcep Gaussova eliminacija pivotiranje matrices linear equations LU decomposition Gauss elimination pivoting true true false [A. Jurgec] Slovenski jezik Angleški jezik Diplomsko delo 2009-09-16 12:37:26 2009-11-17 11:38:48 2022-04-12 00:11:09 2022-04-18 03:26:50 2009 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 17178632 URN:SI:UM:DK:HYYLYZCD UNI_Jurgec_Anja_2009.pdf UNI_Jurgec_Anja_2009.pdf 1 18E15B3A75EE10B9217E3AA3F0C9B334 cf7d2fa16a7db00b75e9ba79ae120f81ee1a890ecb65baa566217ff871f12b85 37f8c22d-7c03-11eb-bb7a-00155d0001ca 20.500.12556/dkum/a232ea19-4b25-451d-b5aa-3a7d929c4334 https://dk.um.si/Dokument.php?lang=slv&id=10693 Fakulteta za naravoslovje in matematiko 0 0 0