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MathGroup Archive 2005

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Re: Re: Limit of list

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57626] Re: [mg57527] Re: Limit of list
  • From: DrBob <drbob at bigfoot.com>
  • Date: Thu, 2 Jun 2005 05:17:06 -0400 (EDT)
  • References: <d79ejm$lb1$1@smc.vnet.net> <200505310859.EAA03396@smc.vnet.net> <opsrnpltapiz9bcq@monster.ma.dl.cox.net> <p06210287bec30fedd446@[130.95.156.21]>
  • Reply-to: drbob at bigfoot.com
  • Sender: owner-wri-mathgroup at wolfram.com

> Not COMPLETELY undocumented.

Ah. F1 doesn't work, and neither does the recently advertised Google trick for searching the current documentation online. Unrestricted Google DOES work, on the other hand, but I didn't try that until now. Sigh...

>> Just as well, I guess, since it can't possibly work.
> Why not?

Because a finite sequence has an uncountable number of extensions, most of which don't converge, others of which converge to anything one cares to arbitrarily choose. SequenceLimit simply gives an answer to the question, "What is the result of Wynn's epsilon algorithm for this list of numbers?" Since I've never heard of the algorithm until now, it's not likely I would ask that question.

SAT questions that ask, "What's the next term in this sequence?" are written by mathematical morons who (apparently) don't realize all the choices are equally valid.

Bobby

On Wed, 1 Jun 2005 15:13:49 +0800, Paul Abbott <paul at physics.uwa.edu.au> wrote:

>> SequenceLimit. Another COMPLETELY undocumented feature.
>
> Not COMPLETELY undocumented. Try
>
>    ?SequenceLimit
>
>> Just as well, I guess, since it can't possibly work.
>
> Why not? SequenceLimit returns the approximation given by Wynn's
> epsilon algorithm to the limit of a sequence whose first few terms
> are given by list. This algorithm can give finite results for
> divergent sequences. As I understand it, SequenceLimit is used by
> NIntegrate when Method->Oscillatory.
>
> Cheers,
> Paul
>
>
>>
>> Bobby
>>
>> On Tue, 31 May 2005 04:59:40 -0400 (EDT), Paul Abbott
>> <paul at physics.uwa.edu.au> wrote:
>>
>>> In article <d79ejm$lb1$1 at smc.vnet.net>,
>>>  Guy Israeli <guyi1 at netvision.net.il> wrote:
>>>
>>>> Is there a way to find out the convergence point of a list of numbers?
>>>>
>>>> for example if I have
>>>>
>>>> {1,2,5,6,8,9,10,11,10,11,12,11,12.. and so on}
>>>>
>>>> it will give me something around 10-12
>>>
>>> Try SequenceLimit:
>>>
>>>   SequenceLimit[{1,2,5,6,8,9,10,11,10,11,12,11,12}]
>>>
>>> Also, if your list is entering a cycle there have been previous
>>> MathGroup postings on methods for detecting cycles.
>>>
>>> Cheers,
>>> Paul
>>>
>>
>>
>>
>> --
>> DrBob at bigfoot.com
>
>
>
>
>



-- 
DrBob at bigfoot.com


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