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<H1>Horner's rule</H1>
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(algorithm)

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<strong>Definition:</strong>
A polynomial A(x) = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x<sup>2</sup> + a<sub>3</sub>x<sup>3</sup> +  ... may be written as A(x) = a<sub>0</sub> + x(a<sub>1</sub> + x(a<sub>2</sub> + x(a<sub>3</sub> +  ...))).
<P><em>Note:
A polynomial may be evaluated at a point x', that is A(x') computed, in <a href="theta.html" tppabs="http://hissa.nist.gov/dads/HTML/theta.html"><em> <img src="Theta-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Theta.gif"  border=0 height=10 width=8  alt="Capital Theta">(n)</em></a> 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.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Tue Aug 10 10:09:00 1999.<BR>
HTML page formatted Wed Dec 22 09:35:31 1999.

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