Interpolatory quadrature formulae with Chebyshev abscissae of the third or fourth kind

Journal of Computational and Applied Mathematics

Volumn 81, Issue 1, 1997, Pages 83-99

  Notaris, Sotirios E ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

Chebyshev abscissae; Interpolatory quadrature formulae

Indexed keywords

CHEBYSHEV APPROXIMATION; CONVERGENCE OF NUMERICAL METHODS; ERRORS; FUNCTIONS; POLYNOMIALS;

CHEBYSHEV ABSCISSAE; INTERPOLATORY QUADRATURE FORMULAE;

INTEGRAL EQUATIONS;

EID: 0031164606     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00018-6     Document Type: Article

References (21)

1. G. Akrivis and K.-J. Förster, On the definiteness of quadrature formulae of Clenshaw-Curtis type, Computing 33 (1984) 363-366.
2. N.K. Basu, Evaluation of a definite integral using Tschebyscheff approximation, Mathematica 13 (36) 1 (1971) 13-23.
3. H. Brass, Eine Fehlerabschätzung zum Quadraturverfahren von Clenshaw und Curtis, Numer. Math. 21 (1973) 397-403.
4. H. Brass and G. Schmeisser, The definiteness of Filippi's quadrature formulae and related problems, in: G. Hämmerlin, ed., Numerische Integration, Internat. Ser. Numer. Math., Vol. 45 (Birkhäuser, Basel, 1979), pp. 109-119.
5. H. Brass and G. Schmeisser, Error estimates for interpolatory quadrature formulae, Numer. Math. 37 (1981) 371-386.
6. C.W. Clenshaw and A.R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960) 197-205.
7. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic Press, San Diego, 1984, 2nd ed.).
8. L. Fejér, Mechanische Quadraturen mit positiven Cotesschen Zahlen, Math. Z. 37 (1933) 287-309.
9. W. Gautschi, Numerical quadrature in the presence of a singularity, SIAM J. Numer. Anal. 4 (1967) 357-362.
10. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, San Diego, 1980, 4th ed.).
11. M. Kütz, A note on error estimates for the Clenshaw-Curtis and other interpolatory quadratures, Analysis 4 (1984) 45-51.
12. F. Locher, Fehlerabschätzungen für das Quadraturverfahren von Clenshaw und Curtis, Computing 4 (1969) 304-315.
13. G. Pólya, Über die Konvergenz von Quadraturverfahren, Math. Z. 37 (1933) 264-286.
14. P. Rabinowitz, Gaussian integration in the presence of a singularity, SIAM J. Numer. Anal. 4 (1967) 191-201.
15. P. Rabinowitz, Numerical integration in the presence of an interior singularity, J. Comput. Appl. Math. 17 (1987) 31-41.
16. P. Rabinowitz, On the convergence of closed interpolatory integration rules based on the zeros of Gegenbauer polynomials, J. Comput. Appl. Math. 17 (1987) 43-46.
17. P. Rabinowitz, Personal communication.
18. V.A. Steklov, On the approximate calculation of definite integrals with the aid of formulas of mechanical quadrature, Izv. Akad. Nauk SSSR (6) 10 (1916) 169-186 (in Russian).
19. G. Szegö, Asymptotische Entwicklungen der Jacobischen Polynome, Schriften der Königsberger Gelehrten Gesellschaft, naturwissenschaftliche Klasse 10 (1933) 35-112; also in: R. Askey, ed., Gabor Szegö: Collected papers, Vol. 2, pp. 401-477.
20. G. Szegö, Asymptotische Entwicklungen der Jacobischen Polynome, Schriften der Königsberger Gelehrten Gesellschaft, naturwissenschaftliche Klasse 10 (1933) 35-112; also in: R. Askey, ed., Gabor Szegö: Collected papers, Vol. 2, pp. 401-477.
21. G. Szegö, Orthogonal Polynomials, Colloquium Publications, Vol. 23 (American Mathematical Society, Providence, RI, 1975, 4th ed.).