Radial Basis Functions: L -approximation orders with scattered centres

نویسندگان

  • Martin D. Buhmann
  • Amos Ron
چکیده

In this paper we generalize several results on uniform approximation orders with radial basis functions in (Buhmann, Dyn and Levin, 1993) and (Dyn and Ron, 1993) to L-approximation orders. These results apply, in particular, to approximants from spaces spanned by translates of radial basis functions by scattered centres. Examples to which our results apply include quasi-interpolation and least-squares approximation from radial function spaces.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Radial Basis Function Approximation: from Gridded Centers to Scattered Centers Radial Basis Function Approximation: from Gridded Centers to Scattered Centers

The paper studies L 1 (IR d)-norm approximations from a space spanned by a discrete set of translates of a basis function. Attention here is restricted to functions whose Fourier transform is smooth on IR d n0, and has a singularity at the origin. Examples of such basis functions are the thin-plate splines and the multiquadrics, as well as other types of radial basis functions that are employed...

متن کامل

Improved error bounds for scattered data interpolation by radial basis functions

If additional smoothness requirements and boundary conditions are met, the well–known approximation orders of scattered data interpolants by radial functions can roughly be doubled.

متن کامل

Scattered Data Modelling Using Radial Basis Functions

Radial basis functions are traditional and powerful tools for multivariate interpolation from scattered data. This self-contained talk surveys both theoretical and practical aspects of scattered data fitting by radial basis functions. To this end, basic features of the radial basis function interpolation scheme are first reviewed, such as well-posedness, numerical stability and approximation or...

متن کامل

Radial basis function approximation: from gridded centers to scattered centers

The paper studies L∞(IR )-norm approximations from a space spanned by a discrete set of translates of a basis function φ. Attention here is restricted to functions φ whose Fourier transform is smooth on IR\0, and has a singularity at the origin. Examples of such basis functions are the thin-plate splines and the multiquadrics, as well as other types of radial basis functions that are employed i...

متن کامل

Scattered data approximation of fully fuzzy data by quasi-interpolation

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003