Lobatto-type quadrature formula in rational spaces

Journal of Computational and Applied Mathematics

Volumn 94, Issue 1, 1998, Pages 1-12

  Min, G ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Chebyshev polynomials; Lobatto type quadrature; Prescribed poles; Rational space

Indexed keywords

POLES AND ZEROS; SET THEORY; THEOREM PROVING;

CHEBYSHEV POLYNOMIALS; LOBATTO QUADRATURE FORMULA;

POLYNOMIALS;

EID: 0032115390     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00068-5     Document Type: Article

References (18)

1. N.I. Achiezer, Theory of Approximation, Ungar, New York, 1956.
2. P. Borwein, T. Erdélyi, Polynomials and Polynomial Inequalities, Springer, New York, 1995.
3. P. Borwein, T. Erdélyi, J. Zhang, Chebyshev polynomials and Markov-Bernstein type inequalities for the rational spaces, J. London Math. Soc. 50 (1994) 501-519.
4. A. Bultheel, P. González, E. Hendriksen, O. Njåstad, Orthogonal rational functions and quadrature on the unit circle, Numer. Algorithms 3 (1992) 105-116.
5. A. Bultheel, P. González, E. Hendriksen, O. Njåstad, Numerical quadratures on the unit circle, a survey with some new results, Orthogonal Polynomials on the Unit Circle: Theory and Application, Univ. Carlos III, Madrid, 1995, pp. 1-20.
6. P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd edn., Academic Press, New York, 1984.
7. E. Egerváry, P. Turán, Notes on interpolation: V, on the stability of interpolation, Acta Math. Acad. Sci. Hungar. 9 (1958) 259-267.
8. W. Gautschi, Gauss-type quadrature rules for rational functions, in: H. Brass, G. Hammerlin (Eds.), International Series of Numerical Mathematics, vol. 112, Birkhäuser Verlag, Basel, 1993, pp. 111-130,
9. W. Gautschi, On the computation of generalize Fermi-Dirac and Bose-Einstein integrals, Comput. Phys. Comm. 74 (1993) 233-238.
10. S. Karlin, W.J. Studden, Tchebycheff Systems, with Applications in Analysis and Statistics, Interscience New York, 1966.
11. G. Min, Hermite-Fejér interpolation in rational systems, Constructive Approx., in press.
12. G. Min, Inequalities for rational functions with prescribed poles, Can. J. Math 50 (1998) 152-166.
13. G. Min, On the denseness of rational systems, J. Approx. Theory, to appear.
14. T.J. Rivlin, Chebyshev Polynomials, 2nd edn., Wiley, New York, 1990.
15. K.D. Sharma, Numerical solution of linear differential equations and Volterra's integral equation using Lobatto quadrature formulae, J. Austral. Math. Soc. 11 (1970) 115-128.
16. J. Szabados, P. Vértesi, Interpolation of Functions, World Scientific, Singapore, 1990.
17. P. Szász, On quasi-Hermite-Fejér interpolation, Acta Math. Acad. Sci. Hungar. 10 (1959) 413-439.
18. W. Van Assche, I. Vanherwegen, Quadrature formulas based on rational interpolation, Math. Comput. 61 (1993) 765-783.