As we add one more point to the list of interpolated points, Eq. (1) tells us how to compute the value of the new interpolating polynomial. The matrix structure of the interpolating table suggests introducing a matrix to hold the th row and th column in the format

for for each and with the initial values .

We leave the construction of the pseudocode and the computer code as an exercise. With care the algorithm can be designed so it keeps only one column of the matrix, saving computer memory. The trick is to run the inner loop over backwards so the fresh values for the th column do not overwrite values still needed from the st column.