The first Matlab function is used to evaluate the coefficient of the Hermite polynomial by divided_difference % ((x,y) are the vectors of data Input: x, y, dy, points (x_i,f(x_i))) Output: b %b_i is the i-th coefficient of the Hermite polynomial in Newton form Pseudocode: Step 1: Set n = length(x), initalize F(1:2:end,1) = y; F(2:2:end, 1) = y; F(2:2:end 2) = dy; X = zeros(2*n,1); X(1:2:end) = x; X(2:2:end) = x; Step 2: Use a for-loop to calclate the second colmun of F Step 3: Use a for-loop (with a sub-loop) to calclate the F Step 4: b = diag(F)