Comments on: Economizing approximations http://www.johndcook.com/blog/2010/02/18/economizing-approximations/ The blog of John D. Cook Sat, 11 Feb 2012 01:10:06 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Phil http://www.johndcook.com/blog/2010/02/18/economizing-approximations/comment-page-1/#comment-107712 Phil Wed, 12 Oct 2011 20:07:29 +0000 http://www.johndcook.com/blog/?p=4600#comment-107712 The factored approach to polynomial evaluation is known as Horner's Method. It may be fewer operations than the naive approach, but that's misleading if you're not computing by hand. On modern computers, flops are free. You actually want to optimize for the shallowest expression, which runs directly counter to what Horner's method does. I have a benchmark for a few different methods available in git://charm.cs.illinois.edu/users/phil/polyeval.git constructed when the professor in my Numerical Analysis class described Horner's Method in the same misleading terms. The factored approach to polynomial evaluation is known as Horner’s Method. It may be fewer operations than the naive approach, but that’s misleading if you’re not computing by hand. On modern computers, flops are free. You actually want to optimize for the shallowest expression, which runs directly counter to what Horner’s method does.

I have a benchmark for a few different methods available in git://charm.cs.illinois.edu/users/phil/polyeval.git constructed when the professor in my Numerical Analysis class described Horner’s Method in the same misleading terms.

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