Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Prevezianos Panagiotis-Emmanouil
Supervisors info:
Σωτήριος Νοτάρης, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Βασίλειος Δουγαλής, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Μιχαήλ Δρακόπουλος, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
The error term of quadrature formulae for analytic functions
Translated title:
The error term of quadrature formulaefor analytic functions
Summary:
In certain spaces of analytic functions, the error term of a quadrature formula is a bounded linear functional. The purpose of this thesis is to provide the methods used in order to compute explicitly the norm of the error functional, which subsequently can be used in order to derive estimates for the error term. In the first chapter, an introduction is made to orthogonal polynomials, presenting some of their most important properties and making a special reference to Chebyshev polynomials. The second chapter deals with quadrature formulae, focusing, mainly, on Gauss quadrature formulae, along with some crucial properties, which indicate their superiority compared to other quadrature formulae. This chapter concludes with the computation of the nodes and weights of the Gauss-Chebyshev quadrature formula of any of the four kinds. The third chapter is dedicated to estimating the error in Gauss quadrature formulae for analytic functions, which is done by Hilbert space methods or contour integration techniques. Finally, in the fourth chapter, some numerical experiments are carried out, which demonstrate the effectiveness of the bounds obtained in the previous chapter.
Main subject category:
Science
Keywords:
numerical integration, orthogonal polynomials, analytic functions, error terms
