Spline Toolbox

Discretization

We collocate at two sites per polynomial piece, i.e., at eight sites altogether. This, together with the two side conditions, gives us 10 conditions, which matches the 10 degrees of freedom.

We choose the two Gaussian sites for each interval. For the standard interval [-.5,.5] of length 1, these are the two sites

• gauss = [-1; 1]/(sqrt(3)*2);
  

From this, we obtain the whole collection of collocation sites by

• ninterv = length(breaks)-1; 
  temp = ((breaks(2:ninterv+1)+breaks(1:ninterv))/2); 
  temp = temp([1 1],:) + gauss*diff(breaks); 
  colpnts = temp(:).';
  

Approximation Space

Numerical Problem