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

• Autorzy: C. de Boor
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)
• 41A10: Approximation by polynomials
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A05: Interpolation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 72
• Numer: 1
• Strony: 49-55

Daty

wydano

2006

Twórcy

autor

C. de Boor

• POB 1076, Eastsound, WA 98245, U.S.A.

Identyfikatory

DOI

10.4064/bc72-0-3