Horner's Rule

A rule for Polynomial computation which both reduces the number of necessary multiplications and results in less numerical instability due to potential subtraction of one large number from another. The rule simply factors out Powers of $x$, giving

$$a_n x^n+a_{n-1}x^{n-1}+\ldots+a_0 = ((a_n x+a_{n-1})x+\ldots)x+a_0.$$

References

Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 9, 1991.