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MathGroup Archive 2003

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Re: Trigonometric math functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44586] Re: Trigonometric math functions
  • From: drbob at bigfoot.com (Bobby R. Treat)
  • Date: Sat, 15 Nov 2003 02:05:14 -0500 (EST)
  • References: <boig47$og2$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Here's a much better Pade approximation, if you're willing to build a
little more complexity into your function (including a square root).
It eliminates the vertical at x==1, and that helps a lot.

<< "Calculus`Pade`"
<< "Graphics`Colors`"
rootPade = Sqrt[1 - x^2]*Pade[ArcCos[x]/Sqrt[1 - x^2], 
    {x, 0, 6, 6}]
Plot[Evaluate[rootPade - ArcCos[x]], {x, 0, 1}, 
  PlotStyle -> {Red, Blue, Black}, PlotRange -> All]

There's a temptation to use Simplify when defining rootPade. But if
you do, the result isn't as robust numerically:

rootPade = Simplify[Sqrt[1 - x^2]*
    Pade[ArcCos[x]/Sqrt[1 - x^2], {x, 0, 6, 6}]]
Plot[Evaluate[rootPade - ArcCos[x]], {x, 0, 1}, 
  PlotStyle -> {Red, Blue, Black}, PlotRange -> All]

Bobby

"Bruno" <bpa at BPASoftware.com> wrote in message news:<boig47$og2$1 at smc.vnet.net>...
> Hi all,
> 
> I would like to implement an arc cos function on a 16 bits µcontroller
> (optimized sin() and cos() function are welcome).
> 
> Does someone have some sources or an algorythm in this way ?
> 
> Thanks in advance,
> 
> Regards.


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