Constructive Polynomial Approximation on the Sphere

Journal of Approximation Theory

Volumn 103, Issue 1, 2000, Pages 91-118

  Sloan, Ian H ^a   Womersley, Robert S ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002700734     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1999.3426     Document Type: Article

References (20)

1. Bajnok B. Construction of designs on the 2-sphere. Europ. J. Combinatorics. 12:1991;377-382.
2. Berman D. L. On a class of linear operators. Dokl. Akad. Nauk SSSR. 85:1952;13-16.
3. Bos L. Some remarks on the Fejér problem for Lagrange interpolation in several variables. J. Approx. Theory. 60:1990;133-140.
4. Clenshaw C. W., Curtis A. R. A method for numerical integration on an automatic computer. Numer. Math. 2:1960;197-205.
5. Daugavet I. K. Some applications of the Marcinkiewicz-Berman identity. Vestnik Leningrad Univ. Math. 1:1974;321-327.
6. Davis P. J. Interpolation and Approximation. 1963;Blaisdell, New York.
7. Driscoll J. R., Healy D. M. Jr. Computing Fourier transforms and convolutions on the 2-sphere. Adv. in Appl. Math. 15:1994;202-250.
8. Fejér L. Mechanische Quadraturen mit positiven Cotesschen Zahlen. Math. Z. 87:1933;287-308.
9. Freeden W., Gervens T., Schreiner M. Constructive Approximation on the Sphere. 1998;Clarendon Press, Oxford.
10. Ganesh M., Graham I., Sivaloganathan J. A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity. SIAM J. Numer. Anal. 31:1994;1378-1414.
11. Gronwall T. H. On the degree of convergence of Laplace's series. Trans. Amer. Math. Soc. 15:1914;1-30.
12. Imhof J. P. On the method for numerical integration of Clenshaw and Curtis. Numer. Math. 5:1963;138-141.
13. Kushpel A. K., Levesley J. Tech. rep. 1998.
14. Müller C. Spherical Harmonics. Lecture Notes in Mathematics. 17:1966;Springer Verlag, Berlin/New York.
15. Reimer M. Interpolation on the sphere and bounds for the Lagrangian square sums. Results in Mathematics. 11:1987;144-166.
16. Reimer M. Constructive Theory of Multivariate Functions. 1990;BI Wissenschaftsverlag, Mannheim/Wien/Zürich.
17. Sloan I. H. Polynomial interpolation and hyperinterpolation over general regions. J. Approx. Theory. 83:1995;238-254.
18. Sloan I. H. Interpolation and hyperinterpolation on the sphere. Haussmann W., Jetter K., Reimer M. Multivariate Approximation: Recent Trends and Results. 1997;255-268 Akademie Verlag GmbH, Berlin (Wiley-VCH).
19. Stroud A. H. Approximate Calculation of Multiple Integrals. 1971;Prentice-Hall, Englewood Cliffs.
20. Szegö G. Orthogonal Polynomials. American Mathematical Society Colloquium Publications. 23:1975;American Mathematical Society, Providence.