Quadrature rules based on partial fraction expansions

Numerical Algorithms

Volumn 24, Issue 1-2, 2000, Pages 159-178

  Weideman, J A C ^a   Laurie, D P ^b  

^a STELLENBOSCH UNIVERSITY   (South Africa)

^b NORTH WEST UNIVERSITY   (South Africa)

Author keywords

Quadrature; Rational interpolation

Indexed keywords

EID: 0034389352     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019145327098     Document Type: Article

References (12)

1. M. Branders and R. Piessens, An extension of Clenshaw-Curtis quadrature, J. Comput. Appl. Math. 1 (1975) 55-65.
2. F. Cala Rodriguez, R. Gonzalez-Vera and M. Jimenez Paiz, Quadrature formulas for rational functions, to appear in Electron. Trans. Numer. Anal.
3. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic Press, New York, 1984).
4. W. Gautschi, Gauss-type quadrature rules for rational functions, in: Numerical Integration IV, eds. H. Brass and G. Hämmerlin, International Series of Numerical Mathematics, Vol. 112 (Birkhäuser, Basel, 1993) pp. 111-130.
5. W. Gautschi, Algorithm xxx: GQRAT - Gauss quadrature for rational functions, to appear in ACM Trans. Math. Software.
6. P. González-Vera, M. Jiménez Paiz, R. Orive and G. López Lagomasino, On the convergence of quadrature formulas connected with multipoint Padé-type approximation, J. Math. Anal. Appl. 202 (1996) 747-775.
7. N.J. Higham, The accuracy of floating point summation, SIAM J. Sci. Comput. 14 (1993) 783-799.
8. V.I. Krylov, Approximate Calculation of Integrals (Macmillan, New York, 1962).
9. F.W.J. Olver, Numerical solution of second-order linear difference equations, J. Res. NBS B 71 (1967) 111-129.
10. R.A. Sack and A.F. Donovan, An algorithm for Gaussian quadrature given modified moments, Numer. Math. 18 (1972) 465-478.
11. W. Van Assche and I. Vanherwegen, Quadrature formulas based on rational interpolation, Math. Comp. 61 (1993) 765-783.
12. J.C. Wheeler, Modified moments and Gaussian quadratures, Rocky Mountain J. Math. 4 (1974) 287-296.