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Article information
2004 , Volume 9, Special issue, p.13-20
Moeller H.M.
An inverse problem for cubature formulae
Having a linear functional over the space of real polynomials in n variables of degree at most d, the question is under what conditions an integral I exists, such that for all , i.e.~such that C can be considered as cubature sum of a formula of degree at least d. In the present paper we study the extension to positive, especially to strictly positive functionals and apply it to investigate the sharpness of the lower bounds given in [5] for the number of nodes in cubature formulae for bivariate integrals.
Classificator Msc2000:- *65D30 Numerical integration
- 65D32 Quadrature and cubature formulas
- 41A55 Approximate quadratures
Keywords: square positive functional, real ideal, annihilating polynomial
Author(s):
Moeller H M
Dr. , Professor
Position: Professor
Office: Fachbereich Mathematik der Universit Dortmund
Address: 44221, Germany, Dortmund, FB Mathematik Universit"at Dortmund Vogelpothsweg 87
Phone Office: (49) 231 755-3077
E-mail: michael.moeller@math.uni-dortmund.de
Bibliography link:
Moeller H.M. An inverse problem for cubature formulae // Computational technologies. 2004. V. 9. Special issue. Selected papers presented at VII International workshop “Cubature formulae and their applications”. Krasnoyarsk, August 2003. P. 13-20
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