20.500.12556/RUL-186568 Numerično reševanje in uporaba Prokrustovega problema in njegovih posplošitev delo diplomskega seminarja Numerical solution and applications of the Procrustes problem and its generalizations Prokrustov problem je matrični optimizacijski problem, pri katerem želimo en nabor podatkov čim bolje prilagoditi drugemu. Za podani matriki $A$ in $B$ v osnovni obliki iščemo tako ortogonalno matriko $Q$, da je matrika $AQ$ čim bliže matriki $B$. Odstopanje med matrikama merimo s Frobeniusovo normo. V nalogi najprej obravnavamo ortogonalni Prokrustov problem in njegovo najpreprostejšo posplošitev, omejeni ortogonalni Prokrustov problem, ter za oba izpeljemo rešitev. Najprej rešitev izpeljemo s pomočjo singularnega razcepa, ki poda preprosto in numerično stabilno rešitev. Predstavimo tudi metodo z Lagrangeovimi multiplikatorji, ki dodatno pojasni teoretično ozadje problema. V nadaljevanju obravnavamo še nekaj pomembnih posplošitev Prokrustovega problema ter primere njegove uporabe. The Procrustes problem is a matrix optimization problem in which we aim to fit one data set to another as closely as possible. Given matrices $A$ and $B$ in their basic form, we seek an orthogonal matrix $Q$ such that the matrix $AQ$ is as close as possible to the matrix $B$. The difference between the matrices is measured using the Frobenius norm. In this thesis, we first consider the orthogonal Procrustes problem and its simplest generalization, the constrained orthogonal Procrustes problem, and derive the solution for both. We first derive the solution using the singular value decomposition, which provides a simple and numerically stable solution. We also present the method of Lagrange multipliers, which further explains the theoretical background of the problem. We then consider several important generalizations of the Procrustes problem and examples of its applications. Prokrustov problem Frobeniusova norma singularni razcep matrike Procrustes problem Frobenius norm singular value decomposition true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2026-09-03 08:15:10 2026-09-03 08:15:18 2026-09-04 04:30:43 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6:512 162533 289844227 23841.pdf 23841.pdf 1 FA6F255DB1225F53574138CB590EA49A 55886dd851dc0772b7687744092a4d1c39612de5f9fce65193cc59efc9647700 683160d6-a75e-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=245843 23842.zip 23842.zip 1 F8BAA872F10178FA9FE840C179E345E7 a57abf84b118fa840dd617c0bf3e800bd261354e45e00783e7171c9bad5f392a 68404c0d-a75e-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=245844 Fakulteta za matematiko in fiziko 0 0 0