Conference paper

Multivariate refinable functions of high approximation order via quotient ideals of Laurent polynomials


Authors listMöller, HM; Sauer, T

Publication year2004

Pages205-228

JournalAdvances in Computational Mathematics

Volume number20

Issue number1-3

ISSN1019-7168

eISSN1572-9044

DOI Linkhttps://doi.org/10.1023/A:1025889132677

ConferenceInternational Workshop on Multivariate Approximation and Interpolation with Applications

PublisherSpringer


Abstract
We give an algebraic interpretation of the well-known "zero-condition" or "sum rule" for multivariate refinable functions with respect to an arbitrary scaling matrix. The main result is a characterization of these properties in terms of containment in a quotient ideal, however not in the ring of polynomials but in the ring of Laurent polynomials.



Citation Styles

Harvard Citation styleMöller, H. and Sauer, T. (2004) Multivariate refinable functions of high approximation order via quotient ideals of Laurent polynomials, Advances in Computational Mathematics, 20(1-3), pp. 205-228. https://doi.org/10.1023/A:1025889132677

APA Citation styleMöller, H., & Sauer, T. (2004). Multivariate refinable functions of high approximation order via quotient ideals of Laurent polynomials. Advances in Computational Mathematics. 20(1-3), 205-228. https://doi.org/10.1023/A:1025889132677



Keywords


Grobner basesLaurent polynomialsquotient idealssubdivision

Last updated on 2025-01-04 at 23:21