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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);
end
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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