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