undergraduate thesis
Quasi - Newton Methods

Milan Milinčević (2016)
Metadata
TitleQuasi - Newtonove metode
AuthorMilan Milinčević
Mentor(s)Kristian Sabo (thesis advisor)
Abstract
U ovom radu ćemo se baviti rješavanjem jednadžbe f(x) = 0 pomoću Newtonove metode tangente te metode sekante, kada nam je funkcija f:\mathbb{R}\rightarrow \mathbb{R}. Za višedimenzionalni problem problem koristit ćemo Newtonovu metodu. Zbog numeričke nestabilnosti Newtonove metode, za višedimenzionalni problem ćemo također koristiti jednu od najpoznatijih tzv. Quasi-Newtonovih metoda, Broydenovu metodu. Objema metodama ćemo rješiti isti primjer te ćemo vidjeti prednosti i nedostatke svake od njih. Reći ćemo nešto još i o dvjema najpoznatijim optimizacijskim Quasi-Newton metodama; Broyden-Fletcher-Goldfarb-Shanno te Davidon-Fletcher-Powell metodi. Pomoću njih ćemo tražiti minimum funkcije f:\mathbb{R}^{n}\rightarrow \mathbb{R}.
KeywordsNewton’s tangent method secant method Newton’s method Jacobian Broyden’s method Hessian Broyden-Fletcher-Goldfarb-Shanno method Davidon-Fletcher-Powell method.
Parallel title (English)Quasi - Newton Methods
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za primijenjenu matematiku
Katedra za primijenjenu matematiku
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Numerical Mathematics
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2016-09-22
Parallel abstract (English)
In this work we will be interested in solving equation f(x) = 0 using Newton’s tangent method and secant method, when we have function f:\mathbb{R}\rightarrow \mathbb{R}. For multidimensional problem we will use Newton’s method. Because of numerical instability of Newton’s method, for multidimensional problem we shall also use one of the best known so-called Quasi-Newton’s method, the Broyden’s method. We will solve the same example with both methods and compare adventages and disadvantages each of them. We shall say something about two best known optimization Quazi-Newton’s methods; BroydenFletcher-Goldfarb-Shanno and Davidon-Fletcher-Powell method. Using them, we will try to minimize function f:\mathbb{R}^{n}\rightarrow \mathbb{R}.
Parallel keywords (Croatian)Newtonova metoda tangente metoda sekante Newtonova metoda Jacobijan Broydenova metoda Hessijan Broyden-Fletcher-Goldfarb-Shanno metoda Davidon-FletcherPowell metoda.
Resource typetext
Access conditionOpen access
Terms of usehttp://creativecommons.org/licenses/by-nc-nd/3.0/hr/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:223297
CommitterMirna Šušak Lukačević