Scattered Date Interpolation from Principal Shift-Invariant Spaces Original Research Article

Under certain assumptions on the compactly supported function φ∈C(Rd), we propose two methods of selecting a function s from the scaled principal shift-invariant space Sh(φ) such that s interpolates a given function f at a scattered set of data locations. For both methods, the selection scheme amounts to solving a quadratic programming problem and we are able to prove error estimates similar to those obtained by Duchon for surface spline interpolation.