NIST

Horner's rule

(algorithm)

Definition: A polynomial A(x) = a0 + a1x + a2x² + a3x³ + … may be written as A(x) = a0 + x(a1 + x(a2 + x(a3 + …))).

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

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

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