Interpolation and approximation on the unit disc by complex harmonic splines
نویسندگان
چکیده
منابع مشابه
Interpolation by Splines on Triangulations
We review recently developed methods of constructing Lagrange and Her-mite interpolation sets for bivariate splines on triangulations of general type. Approximation order and numerical performance of our methods are also discussed.
متن کاملScattered data interpolation by bivariate splines with higher approximation order
Given a set of scattered data, we usually use a minimal energy method to find Lagrange interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. It is known that the approximation order of the minimal energy spline interpolation is only 2 in terms of the size of triangulation. To improve this order of approximation, we propose several new schemes in th...
متن کاملApproximation orders for interpolation by surface splines to rough functions
In this paper we consider the approximation of functions by radial basic function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the interpolation points fill out a bounded domain in Rd . In all of these cases, the analysis takes place in a natural function space dictated by the choice of...
متن کاملOn the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines
This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyhar...
متن کاملOn uniform approximation by splines
for 0 ≤ r ≤ k − 1. In particular, dist (f, S π) = O(|π| ) for f ∈ C(I), or, more generally, for f ∈ C(I), such, that f (k−1) satisfies a Lipschitz condition, a result proved earlier by different means [2]. These results are shown to be true even if I is permitted to become infinite and some of the knots are permitted to coalesce. The argument is based on a “local” interpolation scheme Pπ by spl...
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: 1985
ISSN: 0021-9045
DOI: 10.1016/0021-9045(85)90119-4