(algorithm)

**Definition:**
A polynomial A(x) = a_{0} + a_{1}x + a_{2}x² + a_{3}x³ + … may be written as A(x) = a_{0} + x(a_{1} + x(a_{2} + x(a_{3} + …))).

*Note:
A polynomial may be evaluated at a point x', that is A(x') computed, in Θ(n) time using Horner's rule. That is, repeated multiplications and additions, rather than the naive methods of raising x to powers, multiplying by the coefficient, and accumulating.*

Author: PEB

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Entry modified 17 December 2004.

HTML page formatted Wed Mar 13 12:42:46 2019.

Cite this as:

Paul E. Black, "Horner's rule", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/hornersrule.html