| dc.contributor.advisor |
Milovanović, V. Gradimir |
|
| dc.contributor.author |
Stanić, Marija |
|
| dc.date.accessioned |
2011-07-14T08:26:14Z |
|
| dc.date.available |
2011-07-14T08:26:14Z |
|
| dc.date.issued |
2007-06-05 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/1741 |
|
| dc.description.abstract |
The field of research in this dissertation is consideration of some nonstandard types of orthogonality and their applications to constructions of quadrature rules with maximal degree of exactness, i.e., quadrature rules of Gaussian type. The research in this dissertation is connected with the following subjects: Theory of Orthogonality, Numerical Integration and Approximation Theory. We have tried to produce a balanced work between theoretical results and numerical algorithms. |
en_US |
| dc.description.provenance |
Submitted by Slavisha Milisavljevic (slavisha) on 2011-07-14T08:26:14Z
No. of bitstreams: 1
PhD MS.pdf: 784962 bytes, checksum: dda4487a0720911a700589adc056238b (MD5) |
en |
| dc.description.provenance |
Made available in DSpace on 2011-07-14T08:26:14Z (GMT). No. of bitstreams: 1
PhD MS.pdf: 784962 bytes, checksum: dda4487a0720911a700589adc056238b (MD5)
Previous issue date: 2007-06-05 |
en |
| dc.language.iso |
sr |
en_US |
| dc.publisher |
Kragujevac, Srbija |
en_US |
| dc.title |
Generalisane kvadraturne formule Gauss-ovog tipa |
en_US |
| mf.author.birth-date |
1975 |
|
| mf.author.birth-place |
Gornji Milanovac |
en_US |
| mf.author.birth-country |
Jugoslavija |
en_US |
| mf.author.citizenship |
Srpsko |
en_US |
| mf.author.nationality |
Srpsko |
en_US |
| mf.subject.area |
Mathematics |
en_US |
| mf.subject.keywords |
Approximation theory |
en_US |
| mf.subject.subarea |
Numerical analysis |
en_US |
| mf.contributor.committee |
Milovanović, V. Gradimir |
|
| mf.contributor.committee |
Spalević, M. Miodrag |
|
| mf.contributor.committee |
Cvetković, S. Aleksandar |
|
| mf.university.faculty |
Prirodno-matematički fakultet Univerziteta u Kragujevcu |
en_US |
| mf.document.references |
91 |
en_US |
| mf.document.pages |
VII+139 |
en_US |
| mf.document.location |
Faculty of Science and Mathematics, University of Kragujevac, Serbia |
en_US |
| mf.document.genealogy-project |
Yes |
en_US |
| mf.description.abstract-ext |
This dissertation, beside Preface and References with 91 items, consists of four chapters: 1. Orthogonality and Quadrature Formulae; 2. Orthogonal Systems of Trigonometric Functions; 3. Quadratures with Maximal Trigonometric Degree of Exactness; 4. Numerical Integration of Highly Oscillatory Functions. In Chapter 1 a brief review of the theory of orthogonal polynomials, as well as a review of interpolatory quadrature rules, Gaussian quadrature rules, and their generalizations, are presented. Orthogonal trigonometric polynomials of semi–integer degree are introduced and studied in details in Chapter 2. Chapter 3 is devoted to quadrature rules with maximal trigonometric degree of exactness. At first, quadrature rules with simple nodes are considered. Also, s- and σ-orthogonal trigonometric polynomials of semi–integer degree are introduced and the corresponding quadratures with multiple nodes in the both cases (with equal multiplicities in each nodes and with fixed different multiplicities in each nodes) are considered. In all cases numerical methods for constructing such quadratures are presented. Several numerical examples are also included. Finally, in Chapter 4, Gaussian quadrature rules for some classes of integrands involving highly oscillatory functions are considered. We focus on an idea of using the exponential fitting and solve the existence question of such quadratures, partially. Also, a numerical method for construction of such quadratures is given and some numerical examples are included. |
en_US |