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continued fraction expansion
From: |
Bart Vandewoestyne |
Subject: |
continued fraction expansion |
Date: |
Thu, 27 May 2004 03:46:04 -0500 |
User-agent: |
Mutt/1.3.28i |
Hello all,
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:
>> x = rand
x =
0.6068
>> rat(x)
ans =
1 + 1/(-3 + 1/(2 + 1/(5 + 1/(4 + 1/(14)))))
>> rat(x, 0.0000001)
ans =
1 + 1/(-3 + 1/(2 + 1/(5 + 1/(4 + 1/(14 + 1/(2))))))
The problem is that I don't need the result as a string, rather i need
it as a vector, so in the above two cases this would be something like:
>> rat(x)
ans =
[1 -3 2 5 4 14]
>> rat(x, 0.0000001)
ans =
[1 -3 2 5 4 14 2]
Does anybody know of an implementation for this? Or will I have to look
at how the Matlab script builds the string and try to adapt it to my own
needs?
Thanks,
Bart
PS: the algorithm that calculates the continued fraction expansion up to
a certain number n of digits is easy and can be found at
http://mathworld.wolfram.com/ContinuedFraction.html. I've implemented
it as:
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...
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- continued fraction expansion,
Bart Vandewoestyne <=