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Re: Re: Computation speeds: numerical vs symbolic

  • To: mathgroup at
  • Subject: [mg55928] Re: [mg55925] Re: Computation speeds: numerical vs symbolic
  • From: Andrzej Kozlowski <akoz at>
  • Date: Sun, 10 Apr 2005 23:07:04 -0400 (EDT)
  • References: <d2tfah$ql7$> <>
  • Sender: owner-wri-mathgroup at

On 10 Apr 2005, at 19:54, Jon Harrop wrote:

> AES wrote:
>> So, I'm just curious, how can a calculate and plot command like this
>> be so stunningly fast?  and the trivially simple symbolic integration
>> above be so slow?
> You could think of it as: the numerical work uses finite precision but 
> the
> symbolic work uses infinite precision.
> Put another way, how high does the precision of the numerical routine 
> need
> to be such that symbolic routine is faster?
> -- 
> Dr Jon D Harrop, Flying Frog Consultancy

I do not think viewing symbolic computation as "infinite precision" 
numerical computation really gets to the heart of the matter. In fact, 
in many cases "finite precision" numerical computations will often be 
slower than "infinite precision" ones. This happens when the algorithms 
used are essentially trivial like in this example:


{0.17 Second,Null}



{0.62 Second,Null}

However, most symbolic algorithms are highly non-trivial and usually 
have very high complexity; in fact single exponential complexity  is 
considered to be very reasonable in symbolic algebra.

Andrzej Kozlowski
Chiba, Japan

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