Let $P(x)$ be a polynomial of degree $D$.  Given an evenly spaced input mesh
$x_k$ (i.e. $x_k = x_0 + kh$ for a mesh width $h$) up to $D$ finite differences
may be calculated.  The $D+1$ differences $\Delta^{j}P(x_0)$ are called
\emph{DDA seeds} for P(x_k).  The first $D+1$ polynomial outputs may be
represented as a vector $P$, as may the seeds $c$.  The two are related by the
following matrix $A$:

\begin{eqnarray}
	c &=& A^{-1} P \\
	P &=& A c \\
	A_{ij} = {i \choose j}
\end{equation}

with the definition

\begin{equation}
	{i \choose j} = \left|
	\begin{array}{ll}
		\frac{i!}{j!(i - j)!}, & i >= j; \\
		0, & i < j
	\end{array}
	\right.
\end{equation}

Additionally, there are $D+1$ coefficients of $P(x) = k_0 + k_1 x + k_2 x^2 +
\ldots + k_D x^D$.  We label these coefficients as the vector $K$.
They are related to the vector of the first $D+1$ polynomial outputs
by the van der Monde matrix $V$:

\begin{eqnarray}
	P &=& V K \\
	K &=& V^{-1} P \\
	V_{ij} = x_i^j
\end{equation}

If the input mesh is integral, i.e. $x_k$ = $k$, then $V$ takes a simpler form
which we will call $E$:

\begin{eqnarray}
	P &=& E K \\
	K &=& E^{-1} P \\
	E_{ij} = i^j
\end{equation}

The polynomial outputs may be completely represented in any of these three
ways: By the $D+1$ coefficients $K$, by the $D+1$ outputs $P$, or by the $D+1$
seeds $c$.  The latter is often convenient since it allows one to reproduce the
polynomial outputs, for many more mesh points than just the first $D+1$, using
only addition.  A DDA thus allows efficient evaluation of polynomials by
circumventing the need for floating-point multiplies.  Further efficiency may
be obtained if the addition is done in fixed-point.