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

DOI10.1023/A:1025889132677zbMath1054.65135OpenAlexW166745824MaRDI QIDQ1424953

Thomas Sauer, Hans-Michael Möller

Publication date: 15 March 2004

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1025889132677

zbMATH Keywords

waveletsGröbner basesLaurent polynomialssubdivisionscaling matrixmultivariate refinable functionsquotient ideals

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Numerical methods for wavelets (65T60)

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Anisotropic bivariate subdivision with applications to multigrid ⋮ Decompositions of trigonometric polynomials with applications to multivariate subdivision schemes ⋮ Multiple multivariate subdivision schemes: matrix and operator approaches ⋮ From Hermite to stationary subdivision schemes in one and several variables ⋮ Vector multivariate subdivision schemes: comparison of spectral methods for their regularity analysis ⋮ Multivariate refinable functions, differences and ideals -- a simple tutorial ⋮ Kernels of discrete convolutions and application to stationary subdivision operators ⋮ Scalar multivariate subdivision schemes and box splines ⋮ On construction of multivariate wavelets with vanishing moments ⋮ Differentiability of multivariate refinable functions and factorization ⋮ On construction of multivariate wavelet frames

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