Gauss and anti-Gauss quadrature formulae

Postgraduate Thesis uoadl:2885656 567 Read counter

Unit:
Κατεύθυνση Εφαρμοσμένα Μαθηματικά
Library of the School of Science
Deposit date:
2019-11-17
Year:
2019
Author:
Papadopoulos Vasileios
Supervisors info:
Σωτήριος Νοτάρης, Καθηγητής, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών, Μαθηματικό
Original Title:
Gauss and anti-Gauss quadrature formulae
Languages:
English
Translated title:
Gauss and anti-Gauss quadrature formulae
Summary:
The present thesis is about Gauss and anti-Gauss quadrature formulas. It
is well known that many properties of Gauss formula arise from orthogonal
polynomials, therefore, the first chapter is devoted to orthogonal
polynomials along with their properties from both the computational and
theoretical point of view. The second chapter is dedicated to the Gauss
quadrature formula, focusing on its construction and most important
properties, which demonstrate its superiority compared to other quadrature
formulas. The third chapter is devoted to the anti-Gauss quadrature
formula, a highly efficient method, presented by Laurie in order to
practically estimate the error of the Gauss formula. After describing the
formula and its most important properties, we focus on its behaviour for
some of the classical weight functions. In the fourth and final chapter,
the thesis concludes with some numerical examples, for the Legendre and
Jacobi weight functions, which demonstrate the efficiency of anti-Gauss
formula in estimating the error of the Gauss formula.
Main subject category:
Science
Keywords:
Gauss, anti-Gauss, quadrature formulae
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
11
Number of pages:
92
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