Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Karkazis Dimitris
Supervisors info:
Σωτήριος Νοτάρης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Βασίλειος Δουγαλής,Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Μιχάλης Δρακόπουλος,Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
ΤΥΠΟΙ ΑΡΙΘΜΗΤΙΚΗΣ ΟΛΟΚΛΗΡΩΣΗΣ ΓΙΝΟΜΕΝΟΥ ΜΕ ΣΥΝΑΡΤΗΣΗ ΒΑΡΟΥΣ ΚΑΙ ΚΟΜΒΟΥΣ CHEBYSHEV
Translated title:
PRODUCT INTEGRATION RULES FOR CHEBYSHEV WEIGHT FUNCTIONS WITH CHEBYSHEV ABSCISSAE
Summary:
We study three product integration rules, for the Chebyshev weight function of the second-kind based on the Chebyshev abscissae of the first, third and fourth-kind. The new rules are shown to have positive weights gievn by explicit formulae. Furthermore, we determine the precise degree of exactness and we compute the variance of the quadrature formulae, we examine their defitiness or nondefitiness, and we obtain error bounds for these formulae either asymptotically optimal by Peano kernel methods or for analytic functions by Hilbert space techniques. In addition, the convergence of the quadrature formulae is shown not only for Riemann integrable functions on [-1,1], but also, by generalizing a result of Rabinowitz, for functions having a monotinic singularity at one or both endpoints of [-1,1].
Main subject category:
Science
Keywords:
Chebyshev, Gauss quadrature, accurate methods, Chebyshev polynomials
