منابع مشابه
On Polyharmonic Interpolation
In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C∞ or analytic functions in the ball BR. We prove two main results on the interpolation of C∞ or analytic functions f in the ball BR by polyharmonic functions h of a given...
متن کاملPolyharmonic spline interpolation on a semi-space lattice
We consider the problem of semi-cardinal interpolation for polyharmonic splines. For absolutely summable data sequences, we construct a solution to this problem using a Lagrange series representation. The corresponding Lagrange functions are deened using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.
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 کاملNote on Polyharmonic Functions1
It is the purpose of this note to show that there exists an inequality of the same general character as (1) if the hypothesis that u(P) be harmonic is replaced by the considerably weaker assumption that u(P) be a polyharmonic function of order « (w>l). The latter expression refers to a function which is continuous, has continuous derivatives up to the order 2«, and is a solution of AMu = 0, whe...
متن کاملPolyharmonic Approximation on the Sphere
The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green’s functions of polyharmonic differential operators. We show that the Lp approximation order for this kind of approximation is σ for functions having Lp smoothness σ (for σ up to the order of the underlying differential operator, just ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.09.038