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 powersof , giving

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.