Spline Toolbox

Choice of Spline Space

We deal with cubic splines, i.e., with order

• k = 4;
  

and use the break sequence

• breaks = [0 1 1.1 3 5 5.5 7 7.1 7.2 8];
  lp1 = length(breaks); 
  

and use simple interior knots, i.e., use the knot sequence

• t = breaks([ones(1,k) 2:(lp1-1) lp1(:,ones(1,k))]);
  

Note the quadruple knot at each end. Since k = 4, this makes [0..8] = [breaks(1)..breaks(lp1)] the interval of interest, with n = length(t)-k the dimension of the resulting spline space . The same knot sequence would have been supplied by

• t=augknt(breaks,k);
  

What Is a Chebyshev Spline?

Initial Guess