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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.


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

© 1996-9 Eric W. Weisstein