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Re: New Analytical Functions - Mathematica Verified

• To: mathgroup at smc.vnet.net
• Subject: [mg66947] Re: New Analytical Functions - Mathematica Verified
• From: dhky at shaw.ca
• Date: Sun, 4 Jun 2006 02:01:35 -0400 (EDT)
• References: <200605280104.VAA23436@smc.vnet.net> <200606011055.GAA20733@smc.vnet.net> <e5osg1$hvp$1@smc.vnet.net> <e5rf0d$h4r$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Mohamed Al-Dabbagh wrote:
> Daniel Lichtblau wrote:
>
> > They will change the behavior of its derivatives. Actually I think I did
> > not want to use the DiracDelta component in that particular definition
> > (or else to use further derivatives thereof in the definition for higher
> > derivatives of FractionalPart).
> > ...........................
> > ...........................
> > Did you try it?
> >
>
> Dan,
>
> Your usage of DiracDelta has made some remarkable correction for the
> result, but on a very high cost of runtime! I have made some
> experiments and wanted to publish them. You should remember that my
> paper:
>
> http://dabbagh2.fortunecity.com/disc
>
> has proved that the derivative of the fractional part of any function
> is the SAME as derivative of that function WITHOUT involving in the
> calculation of fractional part!
>
> When I used your improvement using Dirac Delta, a very substantial
> improvement occurred on the numerical results. HOWEVER, this lead to
> some very long delays. To the extent that calculating 5th derivative of
> the FractionalPart(x^5) to 1000 places of decimal would take about ONE
> HOUR!!!! Here are some results I arranged it in a page prepared for
> you:
>
> http://dabbagh2.fortunecity.com/lichtblau/
>
> You will see how my formulas are A LOT faster.
> 
> 
> Mohamed Al-Dabbagh

• References:
  • Re: New Analytical Functions - Mathematica Verified
    • From: "Mohamed Al-Dabbagh" <mohamed_al_dabbagh@hotmail.com>