Error estimates for matrix-valued radial basis function interpolation
نویسنده
چکیده
We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrixvalued RBFs.
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 کاملApproximation and Interpolation Employing Divergence–free Radial Basis Functions with Applications
Approximation and Interpolation Employing Divergence–free Radial Basis Functions with Applications. (May 2002) Svenja Lowitzsch, Dipl., Georg-August University, Göttingen Co–Chairs of Advisory Committee: Dr. Francis J. Narcowich Dr. Joseph D. Ward Approximation and interpolation employing radial basis functions has found important applications since the early 1980’s in areas such as signal proc...
متن کاملError estimates and condition numbers for radial basis function interpolation
For interpolation of scattered multivariate data by radial basis functions, an \uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich{Ward theory of upper bounds on the norm...
متن کاملMatrix-valued radial basis functions: stability estimates and applications
Radial basis functions (RBFs) have found important applications in areas such as signal processing, medical imaging, and neural networks since the early 1980’s. Several applications require that certain physical properties are satisfied by the interpolant, for example being divergence free in case of incompressible data. In this paper we consider a class of customized (e.g. divergence-free) RBF...
متن کاملA trade-off principle in connection with the approximation by positive definite kernels
A frequently used method to handle scattered data approximation problems on different structures is the interpolation by linear combinations of a single positive definite kernel. Here the underlying positive definite kernel is responsible for the quality of the common estimates of the two main issues in this approximation process. Firstly the approximation error and secondly the stability of th...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 137 شماره
صفحات -
تاریخ انتشار 2005