Publication Cover
Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 2
57
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Construction of cubature formulae with preassigned nodesFootnote§

, &
Pages 233-245 | Received 02 Oct 2006, Accepted 07 Mar 2007, Published online: 26 Feb 2008

References

  • Stroud , AH and Secrest , D . 1966 . Gaussian Quadrature Formulae , Englewood Cliffs, New Jersey : Prentice-Hall .
  • Guessab , A . 1987 . Numerical cubature formulae with preassigned knots . Numerische Mathematik , 52 : 467 – 478 .
  • Morrow , CR and Patterson , TNT . 1985 . The construction of algebraic cubature formulae by the distribution of nodes along selected lines . SIAM Journal of Numerical Analysis , 22 : 1178 – 1190 .
  • Cox , D , Little , J and O'shea , D . 1997 . Ideals, Varieties, and Algorithms, , 2nd Edn , Springer : Berlin .
  • Mysovskikh , IP . 1968 . On the construction of cubature formulae with fewest nodes . Doklady Akademii Nauk SSSR , 178 : 1252 – 1254 . (in Russian); 1968, Soviet Mathematics Doklady, 9, 277–280 (in English).
  • Davis , PJ and Rabinowitz , P . 1975 . Methods of Numerical Integration , New York : Academic Press .
  • Cools , R and Haegemans , A . 1986 . Optimal addition of knots to cubature formulae for planar regions . Numerische Mathematik , 49 : 269 – 274 .
  • Cools , R and Haegemans , A . 1987 . “ Construction of sequences of embedded cubature formulae for circular symmetric planar regions ” . In Numerical Integration , Edited by: Keast , P and Fair-weather , G . 165 – 172 . Dordrecht : Reidel Publishing Company .
  • Cools , R and Haegemans , A . 1988 . An embedded pair of cubature formulas of degree 5 and 7 for the triangle . BIT , 28 : 357 – 359 .
  • Cools , R and Haegemans , A . 1989 . On the construction of multi-dimensional embedded cubature formulae . Numerische Mathematik , 55 : 735 – 745 .
  • Cools , R . 1992 . “ A Survey of methods for constructing cubature formulae ” . In Numerical Integration: Recent Developments, Software and Applications , Edited by: Espelid , TO and Genz , A . 1 – 24 . Dordrecht : Kluwer Academic Publishers .
  • Koornwinder , T . 1975 . “ Two-variable analogues of the classical orthogonal polynomials ” . In Theory and Application of Special Functions , Edited by: Askey , RA . 435 – 495 . New York : Academic Press .
  • Xu , Y . 2000 . Polynomial interpolation in several variables, cubature formulae, and ideals . Advances in Computational Mathematics , 12 : 363 – 376 .
  • Xu , Y . 2000 . Constructing cubature formulae by the method of reproducing kernel . Numerische Mathematik , 85 : 155 – 173 .
  • Meng , Z and Luo , Z . 2005 . The construction of cubature formulae with some knots along the selected algebraic curve . Journal of Information and Computational Science , 2 ( 3 ) : 539 – 546 .
  • Luo , Z and Meng , Z . Cubature formulae over the n-sphere . Journal of Computational and Applied Mathematics , 202 ( 2 ) 511 – 522 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.