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)) == f[xs]. 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         this_coeff = this_coeff * (1 / (xj - xi));
  21       end
  22     end
  23     coefficients(end+1) = this_coeff;
  24   end
  25 end