Memory considerations

This expression leaves us however with some terms with negative indices, for example $x(-1)$ and $x(-2)$ which may not be defined. Our vector $\boldsymbol{x}$ has components $x(0)$, $x(1)$, $x(2)$ and $x(3)$.

The index $j$ for $\boldsymbol{x}$ runs from $j=0$ to $j=3$ since $\boldsymbol{x}$ is meant to represent a third-order polynomial.

Furthermore, the index $i$ runs from $i=0$ to $i=5$ since $\boldsymbol{y}$ contains the coefficients of a fifth-order polynomial. When $i=5$ we may also have values of $x(4)$ and $x(5)$ which are not defined.

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