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Ideal interpolation: Mourrain's condition vs. D-invariance

100%

de Boor C.

Banach Center Publications

2006

tom 72

nr 1

49-55

Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain's characterization requires the polynomial space to be 'connected to 1', a condition that is implied by D-invariance in case the polynomial space is spanned by monomials. We give examples to show that, for more general polynomial spaces, D-invariance and being 'connected at 1' are unrelated, and that Mourrain's characterization need not hold when his condition is replaced by D-invariance.

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1 Banach Center Publications

1 de Boor C.

1 2006

Wyniki wyszukiwania

Ideal interpolation: Mourrain's condition vs. D-invariance