Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
نویسندگان
چکیده
منابع مشابه
An Extension of the Exponential-type Error Bounds for Multiquadric and Gaussian Interpolations
In the 1990’s exponential-type error bounds appeared in the theory of radial basis functions. For multiquadric interpolation it is O(λ 1 d ) as d → 0, where λ is a constant satisfying 0 < λ < 1. For Gaussian interpolation it is O(C d) c′ d as d → 0 where C ′ and c are constants. In both cases the parameter d, called fill distance, measures the spacing of the points where interpolation occurs. T...
متن کاملOn Error Formulas for Multivariate Polynomial Interpolation
In this paper we prove that the existence of an error formula of a form suggested in [2] leads to some very specific restrictions on an ideal basis that can be used in such formulas. As an application, we provide a negative answer to one version of the question posed by Carl de Boor (cf. [2]) regarding the existence of certain minimal error formulas for multivariate interpolation. §
متن کاملOn Error Formulas for Multivariate Interpolation
In this paper we prove that the existence of an error formula of a form suggested in [2] leads to some very specific restrictions on an ideal basis that can be used in such formulas. As an application, we provide a negative answer to one version of the question posed by Carl de Boor (cf. [2]) regarding the existence of certain minimal error formulas for multivariate interpolation.
متن کاملA Multivariate Form of Hardy's Inequality and L P -error Bounds for Multivariate Lagrange Interpolation Schemes
The following multivariate generalisation of Hardy's inequality, that for m ? n=p > 0
متن کاملBounds for orthogonal polynomials for exponential weights
Orthogonal polynomials pn(W ; x) for exponential weights W 2 = e−2Q on a nite or in nite interval I , have been intensively studied in recent years. We discuss e orts of the authors to extend and unify some of the theory; our deepest result is the bound |pn(W ; x)|W (x)|(x − a−n)(x − an)|6C; x∈ I with C independent of n and x. Here a±n are the Mhaskar–Rahmanov–Sa numbers for Q and Q must satisf...
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: Journal of Approximation Theory
سال: 1992
ISSN: 0021-9045
DOI: 10.1016/0021-9045(92)90058-v