The Strang-Fix interpolation error bound in an operator setting
نویسندگان
چکیده
منابع مشابه
Generalized Strang-Fix condition for scattered data quasi-interpolation
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...
متن کاملThe 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...
متن کاملGeneralization of the Strang and Fix Conditions to the Product Operator
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...
متن کاملAn Improved Error Bound for Gaussian Interpolation
It’s well known that there is a so-called exponential-type error bound for Gaussian interpolation which is the most powerful error bound hitherto. It’s of the form |f(x) − s(x)| ≤ c1(c2d) c3 d ‖f‖h where f and s are the interpolated and interpolating functions respectively, c1, c2, c3 are positive constants, d is the fill-distance which roughly speaking measures the spacing of the data points, ...
متن کاملOn the High-Level Error Bound for Gaussian Interpolation
It’s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It’s of the form|f(x)− s(x)| ≤ (Cd) c d ‖f‖h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small ve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Signal Processing Letters
سال: 2000
ISSN: 1070-9908,1558-2361
DOI: 10.1109/97.841156