Accuracy of Several Multidimensional Refinable Distributions
Compactly supported distributions f1, . . . , fr on Rd are refinable if each fi is a finite linear combination of the rescaled and translated distributions fj(Ax-k), where the translates k are taken along a lattice Γ ⊂ Rd and A is a dilation matrix that expansively maps Γ into itself. Refinable dist...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02182165_v6_n5_p482_Cabrelli |
| Aporte de: |
| Sumario: | Compactly supported distributions f1, . . . , fr on Rd are refinable if each fi is a finite linear combination of the rescaled and translated distributions fj(Ax-k), where the translates k are taken along a lattice Γ ⊂ Rd and A is a dilation matrix that expansively maps Γ into itself. Refinable distributions satisfy a refinement equation f(x) = ΣkεΛ ck f(Ax-k), where Λ is a finite subset of Γ, the ck are r × r matrices, and f = (f1, . . . , fr)T. The accuracy of f is the highest degree p such that all multivariate polynomials q with degree(q) < p are exactly reproduced from linear combinations of translates of f1, . . . , fr along the lattice Γ. We determine the accuracy p from the matrices ck. Moreover, we determine explicitly the coefficients yα,i (k) such that xα = Σi=1 r ΣkεΓ yα,i(k) fi(x + k). These coefficients are multivariate polynomials yα,i (x) of degree |α| evaluated at lattice points k ε Γ. |
|---|