A New Version of the Strang-Fix Conditions
نویسندگان
چکیده
منابع مشابه
The Strang and Fix Conditions
Then Strang and Fix conditions are recalled and proved. The Strang and Fix conditions caracterize the approximating properties of a shift invariant localized operator by its ability to reconstruct polynomials. In particular, it is used to relate the number of vanishing moments of a wavelet to the order of approximation provided by the corresponding multiresolution analysis. Article [1] is gener...
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We first recall the linear approximation of Strang and Fix [1], in the context of multiresolution analysis and wavelets. The original theorem is concerned with general finite element approximations. Theorem 1 (Fix-Strang) Let p ∈ N, φ a (bi)orthogonal scaling function, and ψ * its conjugate wavelet. The following three conditions are equivalent • for any 0 ≤ k < p, there exists a polynomial θ k...
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Quasi-interpolation is very useful in the study of the approximation theory and its applications, since the method can yield solutions directly and does not require solving any linear system of equations. However, quasi-interpolation is usually discussed only for gridded data in the literature. In this paper we shall introduce a generalized Strang-Fix condition, which is related to non-stationa...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1993
ISSN: 0021-9045
DOI: 10.1006/jath.1993.1062