Naslov (srp)

Nestandardne anti-Gausove kvadraturne formule

Autor

Petrović, Nevena, 1986-

Doprinosi

Stanić, Marija, 1975-
Tomović Mladenović, Tatjana, 1984-
Bojović, Dejan, 1968-
Tomanović, Jelena, 1987-

Opis (eng)

In this thesis we are considering the generalization of anti-Gaussian quadrature rules,introduced for algebraic polynomials in 1996.The first generalization refers to the extension of these formulas to the space of trigonometric polynomials, with a special attention paid to an even weight function on [−π, π).The main properties of such quadrature rules have been proved, and an effective numerical method for their construction has been presented. That method is based on relationsbetween nodes and weights of the quadrature rule for trigonometric polynomials, and thecorresponding quadrature rule for algebraic polynomials.The second type of generalization presented in this dissertation is related to multipleorthogonality. Namely, the notions of a set of anti-Gaussian and a set of averaged quadrature rules for the optimal set of quadrature rules in Borges’ sense were introduced, aswell as the corresponding class of multiple orthogonal polynomials. The main properties of such quadrature rules and multiple orthogonal polynomials have been proved, andnumerical methods for their constructions have been presented.Both generalizations include some numerical examples, and the extension to the spaceof trigonometric polynomials is completed by a comparison with other available methods.

Opis (srp)

Ova disertacija se bavi generalizacijom anti-Gauss-ovih kvadraturnih formula koje su uvedene 1996. godine na prostoru algebarskih polinoma.Prva generalizacija koja je urađena odnosi se na proširenje ovih formula naprostor trigonometrijskih polinoma, pri čemu je posebna pažnja posvećena parnimtežinskim funkcijama na intervalu [−π, π). Glavne osobine ovih kvadraturnihformula su dokazane i predstavljen je efikasan numerički metod za njihovo konstruisanje. Taj metod je baziran na vezama između čvorova i težinskih koeficijenata kvadraturne formule za trigonometrijske polinome i odgovarajuće kvadraturneformule za algebarske polinome.Druga vrsta generalizacije koja je predstavljena u ovoj disertaciji odnosi se navišestruku ortogonalnost. Naime, uvedeni su pojmovi skupa anti-Gauss-ovih i skupa usrednjenih kvadraturnih formula za optimalni skup kvadraturnih formula u Borges-ovom smislu, kao i odgovarajuća klasa višestruko ortogonalnih polinoma...

Opis (srp)

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Jezik

srpski

Datum

2024

Licenca

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Creative Commons CC BY-NC-ND 3.0 AT - Creative Commons Autorstvo - Nekomercijalno - Bez prerada 3.0 Austria License.

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