Monte Carlo simulacija

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Upotreba Monte Carlo metode u određivanju približne vrijednosti π. Nakon postavljanja 30000 slučajnih točaka, procjena za π je unutar 0.07% od stvarne vrijednosti. To se dešava s približnom vjerojatnošću od 20%.

Monte-Carlo metode su stohastičke (determinističke) simulacijske metode, algoritmi koji s pomoću slučajnih ili kvazislučajnih brojeva i velikog broja izračuna i ponavljanja predviđaju ponašanje složenih matematičkih sustava.

Izvorno su osmišljene u državnom laboratoriju SAD u Los Alamosu nedugo nakon Drugog svjetskog rata. Prvo je elektroničko računalo u SAD-u upravo bilo dovršeno, i znanstvenici u Los Alamosu su razmatrali kako da ga najbolje iskoriste za razvoj termonuklearnog oružja (hidrogenske bombe). Kasne 1946. Stanislav Ulam je predložio korištenje slučajnog uzorkovanja za simuliranje putanja neutrona, a John von Neumann je razvio detaljan prijedlog rane 1947. Ovo je dovelo do simulacija manjih razmjera koje su ipak bile neophodno važne za uspješno dovršenje projekta. Metropolis i Ulam su 1949. objavili rad u kojem su iznijeli svoje ideje, čime su potaknuta velika istraživanja tokom 1950-ih godina. Metoda je dobila naziv po gradu u državici Monako, slavnom po svojim kockarnicama (što je prihvaćeno na prijedlog Nicka Metropolisa, jednog od pionira Monte-Carlo metode).

U ekonomiji se rabe ze proračunavanje poslovnog rizika, promjena vrijednosti investicija, pri strateškom planiranju i slično.

U medicinskoj fizici i radioterapiji koristi se za planiranje doze zračenja tumora.

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