Constructing tight frames of multivariate functions
نویسندگان
چکیده
منابع مشابه
Constructing tight frames of multivariate functions
The paper presents a method of construction of tight frames for L(Ω), Ω ⊂ R. 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 wit...
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We provide a new method for constructing equiangular tight frames (ETFs). This method is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of infinite families of such frames. The construction is extremely simple: a tensor-like combination of a Steiner system and a regular simplex. It provides great fr...
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Integer-translates of compactly supported univariate refinable functions φi , such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions from the φi ’s. The objective of this paper is to in...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2009
ISSN: 0021-9045
DOI: 10.1016/j.jat.2008.01.001