Uniqueness of the Gaussian Quadrature for a Ball

Journal of Approximation Theory

Volumn 104, Issue 1, 2000, Pages 21-44

  Bojanov, B ^a   Petrova, G ^b  

^a UNIVERSITY OF SOFIA   (Bulgaria)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Gauss quadrature formula; orthogonal polynomials; highest degree of precision

Indexed keywords

EID: 0041995290     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1999.3442     Document Type: Article

References (13)

1. Bojanov B., Petrova G. Numerical integration over a disc: A new Gaussian quadrature formula. Numer. Math. 8:1998;39-59.
2. Bojanov B., Petrova G. On minimal cubature formulae for product weight functions. J. Comput. Appl. Math. 85:1997;113-121.
3. B. Bojanov, and, D. Dimitrov, Gaussian extended cubature formulae for polyharmonic functions, Math. Comp, to appear.
4. Gauss C. Methodus Nova Integralium Valories per Approximationem Inveniendi. Comment. Soc. Regiae Sci. Gottingen. Recentiores. 3:1814;163-196.
5. Krein M. The ideas of P. L. Tchebycheff and A. A. Markov in the theory of limiting values of integrals and their further developments. Uspekhi Fiz. Nauk. 1951;3-120.
6. Möller H. Kubaturformeln mit minimaler Knotenzahl. Numer. Math. 25:1976;185-200.
7. Mysovskih I. Interpolatory Cubature Formulas. 1981;Nauka, Moscow.
8. Petrushev P. Approximation by ridge functions and neural networks. SIAM J. Math. Anal. 30:1998;155-189.
9. Ramm A., Katsevich A. The Radon Transform and Local Tomography. 1996;CRC Press, Boca Raton.
10. Szego G. Orthogonal Polynomials. 1959;Amer. Math. Soc. New York.
11. Stroud A., Secrest D. Gaussian Quadrature Formulas. 1966;Prentice-Hall, Englewood Cliffs.
12. Suetin P. Orthogonal Polynomials of Two Variables. 1988;Nauka, Moscow.
13. Xu Y. Lagrange interpolation on Chebyshev points of two variables. J. Approx. Theory. 87:1996;220-238.