FW: Accuracy of numerical calculation of the Gamma and Beta function

 


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From: Richard Fateman [mailto:fateman at cs.berkeley.edu] 
Sent: Saturday, October 11, 2008 4:35 PM
To: 'Stavros Macrakis'
Subject: RE: [Maxima] Accuracy of numerical calculation of the Gamma and
Beta function


Plotting bigfloats usually doesn't make sense.
1. Plotting generally requires that many numerical evaluations take place.
It is better to be fast.
2. Double floats allow for relative error of about 10^(-18).
3. Plotting devices with 1024 distinct points require a relative error of
about 10^(-3), so anything more
than double float is already vast overkill for such a device. Even a device
with 1,000,000 distinct coordinate
positions would not need such precision.
 
If for some reason bigfloats are needed, e.g. for an incredibly unstable
calculation, you could convert them to
ordinary floats before plotting.  Perhaps the plotting routines should do it
automagically.
 
RJF


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From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Stavros Macrakis
Sent: Saturday, October 11, 2008 4:23 PM
To: Adam Majewski
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Accuracy of numerical calculation of the Gamma and
Beta function


On Sat, Oct 11, 2008 at 3:20 AM, Adam Majewski <adammaj1 at o2.pl> wrote:


Does it mean that Maxima can also be used not only as a CAS but also for
numerical calculations ?



Yes, Maxima can be used for calculations using arbitrary-size integers,
arbitrary-size rationals, machine floating-point, and arbitrary-precision
binary floating-points (bigfloats).  Most numerically-oriented systems
handle only machine floating-point, and are optimized for it. 



Sometimes I (in my opinion) it's hard to change fpprec in Maxima, see
for example:
http://commons.wikimedia.org/w/index.php?title=Image:Lemniscates5.png

Is it possible to change it ? ( to do it with simple one command fpprec)



Some parts of Maxima unfortunately don't know about bigfloats, in particular
the plotting routines.  Sorry about that....

           -s