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Re: floating point issue

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86788] Re: [mg86748] floating point issue
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Fri, 21 Mar 2008 01:52:26 -0500 (EST)
  • References: <200803200753.CAA29210@smc.vnet.net>

On Mar 20, 2008, at 3:53 AM, Chris Scullard wrote:

> Hi everyone,
>
> I wonder if I can get some opinions on the best way to deal with this
> precision issue I am having. I define the vectors:
>
> K = {111.5, 10.5, 1.5}
> g={-0.7071068, 0., -0.7071068}
>
> And I need this:
>
> K.Cross[K, g]
>
> to be 0 in accordance with a vector identity. The answer comes out to
> around 1.3 x 10^(-13), which is certainly close to 0 but not close
> enough for what I'm doing. I've tried various things like writing out
> the cross product explicitly without using the functions but the  
> result
> is the same. And using N in various places doesn't seem to help  
> either.
> What's the standard solution for this kind of thing?

Chop

The larger issue is K and g don't have enough precision to satisfy  
your identity, but g looks like it came from some trigonometric  
identities:

g = {Cos[3 Pi/4],0,Cos[3 Pi/4]}

  and K's entries can be expressed as rational numbers:

K = {223/2,21/2,3/2}

So that's your other option, don't take floating point approximations  
to the entries in K and g.

In[215]:= {223/2,21/2,3/2}.Cross[{223/2,21/2,3/2},{Cos[3 Pi/4],0,Cos 
[3 Pi/4]}]
Out[215]= 0

Regards,

Ssezi


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