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Re: continued fraction expansion

From: Przemek Klosowski
Subject: Re: continued fraction expansion
Date: Thu, 27 May 2004 12:27:35 -0400 (EDT)

   During some experimental work, i came across a little problem where
   I would need to get the digits of a continued fraction expansion of
   a real x, up to a certain tolerance.  In Matlab, i can do this as:

   >> rat(x, 0.0000001)

   ans =  1 + 1/(-3 + 1/(2 + 1/(5 + 1/(4 + 1/(14 + 1/(2))))))


   function a = continued_fraction(x, n)

   a = zeros(n,1);

   r = x;
   a(1) = floor(x);
   for i=2:n,
     r = 1./(r-a(i-1));
     a(i) = floor(r);

   My problem is that i don't want to be able to calculate for n digits,
   but i want to calculate up to a certain *tolerance* like in the Matlab
   rat command...

Matlab's tolerance is expressed as |a-x| < tolerance * |x| whereas
your function, on a quick once-over, has the error of better than
10^-(n-1). In other words, n=1-log10(tolerance*abs(x)). Or something
like that.

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