My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Reply
 
LinkBack Thread Tools Display Modes
October 2nd, 2011, 12:47 PM   #1
Newbie
 
Joined: Oct 2011

Posts: 1
Thanks: 0

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
Newbie
 
Joined: Oct 2011

Posts: 12
Thanks: 0

Re: Rational approximation algorithm

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

  My Math Forum > High School Math Forum > Elementary Math

Tags
algorithm, approximation, rational



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Approximation kyry Calculus 2 January 31st, 2014 09:47 PM
Approximation Shamieh Calculus 1 October 9th, 2013 10:09 AM
approximation for the sum Anton29 Applied Math 5 December 28th, 2011 01:11 PM
Exhibition of Self-Approximation Algorithm and Program. omegapoint Applied Math 2 December 22nd, 2010 04:57 AM
Pi Approximation Marcel777 Number Theory 5 September 27th, 2010 11:49 PM





Copyright © 2019 My Math Forum. All rights reserved.