Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Re: Computation speeds: numerical vs symbolic

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55928] Re: [mg55925] Re: Computation speeds: numerical vs symbolic
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 10 Apr 2005 23:07:04 -0400 (EDT)
  • References: <d2tfah$ql7$1@smc.vnet.net> <200504101054.GAA29067@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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
> http://www.ffconsultancy.com
>
>


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:

In[1]:=
With[{x=Sqrt[2]},Table[x^(2*n),{n,1,10000}]];//Timing

Out[1]=
{0.17 Second,Null}

vs.

In[2]:=
With[{x=N[Sqrt[2],20]},Table[x^(2*n),{n,1,10000}]];//Timing

Out[2]=
{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
http://www.akikoz.net/andrzej/index.html
http://www.mimuw.edu.pl/~akoz/


  • Prev by Date: Re: Re: simplified C API call in MathLink
  • Next by Date: Re: cannot evaluate in HelpBrowser (Win XP)
  • Previous by thread: Re: Computation speeds: numerical vs symbolic
  • Next by thread: Re: Computation speeds: numerical vs symbolic