Interpolation by Translates of a Basis Function

نویسنده

  • Will Light
چکیده

Interpolation using radial basis functions has become an established and useful technique in multi-dimensional data tting. It is a special case of interpolation by translates of a basis function. All the methods used in practice have a strong connection with a variational principle. In this paper we provide a straightforward approach to the variational principle, and make some useful practical deductions from the theory.

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

Approximation of a Fuzzy Function by Using Radial Basis Functions Interpolation

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...

متن کامل

A new trust-region algorithm based on radial basis function interpolation

Optimization using radial basis functions as an interpolation tool in trust-region (ORBIT), is a derivative-free framework based on fully linear models to solve unconstrained local optimization, especially when the function evaluations are computationally expensive. This algorithm stores the interpolation points and function values to using at subsequent iterations. Despite the comparatively ad...

متن کامل

Approximation by Radial Basis Functions with Finitely Many Centers

Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that in...

متن کامل

Spaces of Distributions and Interpolation by Translates of a Basis Function

Interpolation with translates of a basis function is a common process in approximation theory. One starts with a single function (the basis function) and a set of interpolation points. The most elementary form of the interpolant then consists of a linear combination of all translates by interpolation points of the basis function. Frequently , low degree polynomials are added to the interpolant....

متن کامل

Interpolation by Basis Functions of Different Scales and Shapes

Under very mild additional assumptions, translates of conditionally positive definite radial basis functions allow unique interpolation to scattered multivariate data, because the interpolation matrices have a symmetric and positive definite dominant part. In many applications, the data density varies locally, and then the translates should get different scalings that match the local data densi...

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 1999