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 
, giving
 |
Horner's Rule
See also
PolynomialExplore with Wolfram|Alpha
References
Borwein, P. and Erdélyi, T. "Horner's Rule." §1.1.E.5 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, p. 8, 1995.Knuth, D. E. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd ed. Reading, MA: Addison-Wesley, pp. 467-469, 1998.Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 9, 1991.Referenced on Wolfram|Alpha
Horner's RuleCite this as:
Weisstein, Eric W. "Horner's Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HornersRule.html