Construction for a class of interpolation multiscaling functions with dilation factor a≥3

Authors:
Lihong Cui;Ruixue Cong
Affiliations:
School of Science, Beijing University of Chemical Technology, Beijing 100029, PR China;School of Science, Beijing University of Chemical Technology, Beijing 100029, PR China and Foundation Department, Harbin Finance College, Harbin 150030, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

This paper is devoted to construction interpolatory multiscaling functions with a general dilation factor a=3. We first show two-scale matrix symbol associated with interpolatory multiscaling functions is reduced to a special form. Also, a characterization on approximation order for the multiscaling functions is described in terms of elements of this special two-scale matrix symbol. Then, an algorithm is provided for constructing compactly supported interpolating multiscaling functions with dilation factor a=3 and higher approximation order. Finally, the associated several families examples with one-parameter or two-parameters are explicitly presented. The optimal parameter values which make multiscaling functions provide the highest regularity are also computed.