Gerlind Plonka, Vasily Strela
Construction of Multi-Scaling Functions with Approximation and Symmetry
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
41A25 Rate of convergence, degree of approximation
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Abstract: This paper presents a new and efficient way to create multi-scaling
functions with given approximation order, regularity, symmetry and
short support. Previous techniques were operating in the time domain
and required the solution of large systems of nonlinear equations.
By switching to the frequency domain and employing the latest
results of the multiwavelet theory we were able to elaborate a
simple and efficient method of construction of multi-scaling
functions. Our algorithm is based on a recently found
factorization of the refinement mask through the two-scale
similarity transform (TST). Theoretical results and new examples
are presented.

Keywords: Approximation order, symmetry, multi-scaling functions, multiwavelets