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April 9th, 2010, 08:56 PM   #1
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Index of a fibonacci number

Given a fibonacci number, is there any efficient way to compute the its position in the sequence ?

I found this on Wikipedia
[img]
http://upload.wikimedia.org/math/4/6/2/ ... ea259e.png
[/img]

But when F very large (more than 10000 digits) there wont be sufficient precision to get the answer correctly .

Is there any way like matrix exponentiation or something that will get me the answer ?
PS: if A= [ [0,1],[1,1] ] .. computing A^n (can be done in O(logn)) will give the nth fibonacci number

Thank you
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April 10th, 2010, 03:21 AM   #2
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Re: Index of a fibonacci number

Hello abhijith,

To find numbers of fibonacci, you can use this

see here for dutch page, quite easily explained, or here for english page in more detail. Will this do?

Hoempa
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April 10th, 2010, 01:17 PM   #3
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Re: Index of a fibonacci number

I think you were trying to find the index of the Fibonacci number. Yes, there are a few ways of doing this. Perhaps the easiest way is,

jason.spade is offline  
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