Constructing tight frames of multivariate functions

Authors:
Say Song Goh;Tim N. T. Goodman;S. L. Lee
Affiliations:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore;Department of Mathematics, The University of Dundee, Dundee DD1 4HN, Scotland, UK;Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore
Venue:
Journal of Approximation Theory
Year:
2009

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Abstract

The paper presents a method of construction of tight frames for L^2(@W),@W@?R^n. The construction is based on local orthogonal matrix extension of vectors associated with the transition matrices across consecutive resolution levels. Two explicit constructions are given, one for linear splines on triangular polygonal surfaces with arbitrary topology and the other for quadratic splines associated with Powell-Sabin elements on a six-direction mesh.