Spline Toolbox

Choice of Sites and Knots

Consider, for example, least squares approximation to given data

. We take the data from a function used extensively by Franke for the testing of schemes for surface fitting (see R. Franke, "A critical comparison of some methods for interpolation of scattered data," Naval Postgraduate School Techn. Rep. NPS-53-79-003, March 1979). Its domain is the unit square. We choose a few more data sites in the -direction than the -direction; also, for a better definition, we use higher data density near the boundary.

• x = sort([[0:10]/10,.03 .07, .93 .97]);
  y = sort([[0:6]/6,.03 .07, .93 .97]);
  [xx,yy] = ndgrid(x,y); z = franke(xx,yy);
  

Example: Approximation by Tensor Product Splines

Least Squares Approximation as Function of y