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


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Entry modified 17 December 2004.
HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:
Paul E. Black, "Horner's rule", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/hornersrule.html

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