divided_difference_coefficients.m

   1 function coefficients = divided_difference_coefficients(xs)
   2   ## Compute divided difference coefficients of `f` at points `xs`.
   3   ##
   4   ## INPUTS:
   5   ##
   6   ##   * ``xs`` - A vector containing x-coordinates.
   7   ##
   8   ## OUTPUTS:
   9   ##
  10   ##   * ``coefficients`` - The vector of coefficients such that
  11   ##   dot(coefficients, f(xs)) == dd. Used to solve linear systems.
  12   ##
  13
  14   coefficients = [];
  15
  16   for xj = xs
  17     this_coeff = 1;
  18     for xi = xs
  19       if (xi != xj)
  20         ## Append (xj - xi) to the vector of coefficients.
  21         this_coeff = this_coeff * (1 / (xj - xi));
  22       end
  23     end
  24     coefficients(end+1) = this_coeff;
  25   end
  26 end