master's thesis
Orthogonal polynomials

Valentina Volmut (2016)
Metadata
TitleOrtogonalni polinomi
AuthorValentina Volmut
Mentor(s)Mihaela Ribičić Penava (thesis advisor)
Abstract
Ortogonalni polinomi su posebna vrsta polinoma koji su otrkiveni prilikom rješavanja određenih diferecijalnih jednadžbi. Cilj ovog diplomskog rada je dati pregled klasičnih ortogonalnih polinoma kao što su: Čebiševljevi polinomi prve i druge vrste, Laguerrovi polinomi, Hermiteovi polinomi i Legendreovi polinomi. Osim definicija, za sve ortogonalne polinome navedene su pripadne funkcije izvodnice i rekurzivne relacije. Završni dio rada posvećen je primjenama ortogonalnih polinoma kod približnog računanja odredenih integrala, odnosno kod Gaussovih kvadraturnih formula koje imaju veliku primjenu u numeričkoj matematici.
KeywordsOrthogonal polynomials Chebyshev Polynomials of the First Kind Chebyshev Polynomials of the Second Kind Hermite Polynomials Laguerre Polynomials Legendre Polynomials Gaussian quadrature formulas
Parallel title (English)Orthogonal polynomials
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Numerical Mathematics
Study programme typeuniversity
Study levelintegrated undergraduate and graduate
Study programmeMathematics and Computer Science
Academic title abbreviationmag. educ. math. et inf.
Genremaster's thesis
Language Croatian
Defense date2016-09
Parallel abstract (English)
Orthogonal polynomials are special type of polynomials which are discovered by solving determinate differencial equations. As a main point of this masters thesis is to represent classical orthogonal polynomials like: Chebyshev Polynomials of the First Kind, Chebyshev Polynomials of the Second Kind, Laguerre Polynomials, Hermite Polynomials and Legendre Polynomials. For this orthogonal polynomials are listed related generating functions and recurrence relations, apart from definitions. Concluding part of this masters thesis is to dedicate application of orthogonal polynomials at approximation calculating definite integral, apropos Gaussian quadrature formulas which have big application in numerical mathematics.
Parallel keywords (Croatian)Ortogonalni polinomi Čebiševljevi polinomi prve vrste Čebiševljevi polinomi druge vrste Laguerrovi polinomi Hermiteovi poli- nomi Legendreovi polinomi Gaussove kvadraturne formule
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:113224
CommitterMirna Šušak Lukačević