The structure of cubature formulae of degree 2 n y 1 is studied from a polynomial ideal point of view. The main result states that if I is a polynomial ideal ลฝ . generated by a proper set of 2 n y 1 -orthogonal polynomials and if the cardinality ลฝ . of the variety V I is equal to the codimension of
โฆ LIBER โฆ
Commuting extensions and cubature formulae
โ Scribed by Ilan Degani; Jeremy Schiff; David J. Tannor
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- English
- Weight
- 233 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0029-599X
No coin nor oath required. For personal study only.
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It has been shown recently that cubature formulae for the unit sphere and for the unit ball are closely related; in particular, cubature formulae for the surface measure on the sphere correspond to formulae for the Chebyshev weight function on the ball. This provides a new method to generate cubatur