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