20.500.12556/RUL-120183 Hitro množenje matrik delo diplomskega seminarja Fast matrix multiplication Množenje matrik je v linearni algebri preprosta operacija, ki se pogosto pojavlja v rešitvah najrazličnejših problemov. Prav zato je bilo v iskanje hitrih algoritmov za množenje matrik vloženega že veliko dela. V diplomskem delu definiramo problem iskanja zgornje meje eksponenta matričnega množenja in razvijemo teorijo ranga in mejnega ranga bilinearnih preslikav. Predstavimo več algoritmov za hitro množenje matrik, ki slonijo na tej teoriji. Izbrane algoritme tudi implementiramo, jih primerjamo med seboj in ocenimo njihovo uporabnost v praksi. Matrix multiplication is one of the most basic operations in linear algebra and thus very common in various scientific disciplines. Consequently, the computation complexity of matrix multiplication has been extensively studied. In this work, we define a problem of finding the upper bound for the exponent of matrix multiplication and present the theory of rank and border rank of bilinear maps. We describe multiple fast matrix multiplication algorithms based on this theory. In the end, we implement some selected algorithms, compare them, and discuss their value in practical applications. množenje matrik eksponent matričnega množenja rang tenzorjev mejni rang matrix multiplication exponent of matrix multiplication tensor rank border rank true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-17 07:16:39 2020-09-17 07:16:41 2024-05-29 14:36:19 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 004 110225 58244355 1468.pdf 1468.pdf 1 E81A320D11990ABA4E12EB67A71C64F6 bc928b6443ca5c6d78bb16c0a0153ced25a554d55b9d408f7410a0d2282ae9e0 05655fb7-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=134963 Fakulteta za matematiko in fiziko 0 0 0