Loading...
Please wait, while we are loading the content...
Similar Documents
Approximation of Polynomials by Radial Basis Functions R. S ch aba ck
| Content Provider | Scilit |
|---|---|
| Author | Laurent, Pierre-Jean Mehaute, Alain Le Schumaker, Larry |
| Copyright Year | 1994 |
| Description | We consider interpolation of real-valued functions / defined on a set Ω C JRd, d > 1. These functions axe interpolated on a set X := {χ χ ,. . . , xnx } of Νχ > 1 pairwise distinct points x 1?. . . , xnx in Ω. Interpolation is done by linear combinations of translates Φ(χ — Xj) of a single continuous real-valued function Φ defined on lRd. For various reasons it is sometimes necessary to add the space of d-variate polynomials of order not exceeding m to the interpolating functions. Interpolation is uniquely possible under the assump tion if p E P ^ satisfies p(x{) = 0 for all x,· E X , then p = 0, (1) D efin ition 1. A function Φ : JRd —► 1R with Φ(—x) = Φ(χ) is conditionally positive definite of order m on JRd if for all sets X = { x i , . . . , xnx } C lRd with Νχ distinct points and all vectors α := (αχ ,. . . , awx ) € 1RNx with ( 2) the quadratic form a j a k $ ( x j —Xk) is always nonnegative, and vanishes only if a = 0. Book Name: Wavelets, Images, and Surface Fitting |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-47245-8&isbn=9780429064241&doi=10.1201/9781439863602-43&format=pdf |
| Ending Page | 482 |
| Page Count | 8 |
| Starting Page | 475 |
| DOI | 10.1201/9781439863602-43 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 1994-07-15 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Wavelets, Images, and Surface Fitting Artificial Intelligence Interpolation Functions Polynomials |
| Content Type | Text |
| Resource Type | Chapter |
