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Topic: computing k-th digit of a real number independently of the previous ones
Replies: 10   Last Post: Jul 1, 2012 4:12 PM

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AMX

Posts: 35
Registered: 8/22/09
Re: computing k-th digit of a real number independently of the
previous ones

Posted: Jun 27, 2012 6:08 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 25 Jun 2012 18:34:04 +0000 (UTC),
Herman Rubin <hrubin@skew.stat.purdue.edu> wrote:

>>> Q: Is it possible to prove the existence of a real number with
>>> the property that in order to compute its k-th digit, we must
>>> compute all the previous ones?

>
>> This is not the property of the number, this is property of way
>> of computation (algorithm) and also representation of the number.


> For many cases, one need not compute the preceding digits,
> but the subsequent ones.

[..]
> Then using number theory, one could get the contribution
> of each term to the desired digit and the subsequent ones,
> and hence compute the k-th digit without computing any
> previosu ones.


How general is this approach? Can I compute 10th and subsequent
decimal digit for Euler number
e = sum 1/n!

AMX




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