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--- gibson:teaching:fall-2016:math753:horner [2016/11/11 11:29]
gibson created
+++ gibson:teaching:fall-2016:math753:horner [2016/11/11 11:37] (current)
gibson
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-====== Horner's method ======
+====== Horner's method for polynomial evaluation ======
 ===Horner's method without base points  ===
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 \end{equation*}
-evaluation only requires 4 adds and 4 multiplies. The payoff gets bigger for higher-order polynomials.
+evaluation only requires 4 adds and 4 multiplies. It's easy to see that these are just two different ways of writing the exact same polynomial. The approach generalizes to arbitrary-order polynomials, and the payoff gets bigger as the order of the polynomial increases.
 === Horner's method with base points ===
@@ Line 28: / Line 28: @@
 The above polynomial is still 4th order, and it is clearly possible to write any polynomial in a form like this for arbitrary $b$'s. The base points require an additional set of subtractions, but it's often worth the trouble, primarily because this is the most natural form for polynomial interpolation via [[gibson:teaching:fall-2016:math753:newtondivdiff|Newton's Divided Differences]].
+Further reading:
+  * [[https://en.wikipedia.org/wiki/Horner%27s_method | Horner's method]] (wikipedia).
+Strangely, there aren't many good online resources for Horner's method. Perhaps it's too simple. so

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