function coefficients = divided_difference_coefficients(xs)
## Compute divided difference coefficients of `f` at points `xs`.
##
## INPUTS:
##
## * ``xs`` - A vector containing x-coordinates.
##
## OUTPUTS:
##
## * ``coefficients`` - The vector of coefficients such that
## dot(coefficients, f(xs)) == f[xs]. Used to solve linear systems.
##
coefficients = [];
for xj = xs
this_coeff = 1;
for xi = xs
if (xi != xj)
this_coeff = this_coeff * (1 / (xj - xi));
end
end
coefficients(end+1) = this_coeff;
end
end