WENDCOEF Function
Computes the coefficients for the Wendland polynomial of type (d,k).
Usage
c = WENDCOEF(d,k)
Input Parameters
d—Positive integer (associated with space dimension).
k—Positive integer (associated with smoothness c2k).
Return Value
c—Array of coefficients for the polynomial c(0) + ... + c(n)*xn.
Discussion
Wendland polynomials serve as compactly supported radial basis functions which are used to build interpolating functions: For given data-space dimension d and interpolant smoothness c2k, the Wendland polynomial of type (d,k) is the unique minimal order polynomial which yields a c2k interpolant and a positive-definite linear system for the RBF coefficients. If WENDCOEF is used to build an RBFIMSCL basis function, then to avoid repeated computation of the polynomial coefficients, it is recommended that the coefficients be computed once and stored in a COMMON block. It is also recommended that if k<5 and the polynomial evaluations are done with POLYEVAL, its Form keyword is used to invoke faster evaluations. But for larger k, the faster evaluations should not be used because they become unstable.
Example
x = INTERPOL([0,1],1001) & d = 0
FOR k=0L,4 DO BEGIN & PLOT,x,POLYEVAL(WENDCOEF(d,k),x,/F) & HAK & END
If Wp(d,k) denotes the Wendland polynomial of type (d,k) then Wp(2*d+1,k) = Wp(2*d,k) for all d. This example shows Wp(0,k) = Wp(1,k) for k=0,1,2,3,4.
