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.