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====== Polynomial Interpolation via Newton Divided Differences ====== \begin{equation*} \left[\begin{array}{ccccc} 1 & & \ldots & & 0 \\ 1 & x_1-x_0 & & & \\ 1 & x_2-x_0 & (x_2-x_0)(x_2-x_1) & & \vdots \\ \vdots & \vdots & & \ddots & \\ 1 & x_k-x_0 & \ldots & \ldots & \prod_{j=0}^{k-1}(x_k - x_j) \end{array}\right] \left[\begin{array}{c} a_0 \\ \\ \vdots \\ \\ a_{k} \end{array}\right] = \left[\begin{array}{c} y_0 \\ \\ \vdots \\ \\ y_{k} \end{array}\right] \end{equation*}