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October 2nd, 2011, 12:47 PM   #1
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Rational approximation algorithm

I'm attempting to write a little program to take a fraction and generate the closest approximate fraction with terms below some limit. Such a tool would come in handy at work for doing arithmetic on small 8-bit processors, but mostly it's a fun exercise.

I have a vague recollection from some long forgotten lecture or textbook concerning a theorem about the "midpoint" fraction. E.g. given two irreducible fractions then are the smallest terms where , or something along those lines.

This would then give me a natural method for finding successively better approximations by first normalizing the sought-after number and starting with the lower bound and upper bound . Then proceed through divide-and-conquer to home in on by successively replacing either the lower bound if or the upper bound if until the term limit is reached.

My only trouble is that I can't seem to remember what the theorem is called or precisely what it states and (more embarrasingly) I haven't been able to prove it to myself. Am I on the right track here?
implicit is offline  
October 12th, 2011, 06:31 PM   #2
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Re: Rational approximation algorithm

I think you may have posted this in the wrong section.
Caligirl711 is offline  

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