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Re: Computation speeds: numerical vs symbolic

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55921] Re: Computation speeds: numerical vs symbolic
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Sun, 10 Apr 2005 06:54:52 -0400 (EDT)
  • References: <d2tfah$ql7$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Perhaps it helps to compare numeric and symbolic integration a 
different way. The time it takes to do a numerical integration obviously 
depends on the number of digits you require. An infinite number of 
digits would require an infinite amount of time.

Consider now, a symbolic integration such as:

Integrate[Exp[-x^2],{x,-\[Infinity],\[Infinity]}]

The answer, Sqrt[Pi], is exact - in effect it contains an infinite 
number of digits - so which is more efficient now?

David Bailey
dbaileyconsultancy.co.uk


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