Re: inverse function computation
- To: mathgroup at smc.vnet.net
- Subject: [mg31689] Re: [mg31660] inverse function computation
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Sat, 24 Nov 2001 16:44:04 -0500 (EST)
- References: <200111231046.FAA24056@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Margot wrote:
>
> Hello,
>
> I'd like to do the following manipulation.
> Let f be a homeomorphism (known explicitly).
> I want Mathematica to compute its inverse f^{-1} and to use it
> for further computations and plots.
> I'm assuming here that f^{-1} is not explicit (take f(x)=x+0.2Sin[x] for
> instance).
>
> I'm not sure that Mathematica has an already built-in function; do you know
> any simple algorithm?
>
> Many thanks
You could do this with explicit inversion via root-finding. One approach
might be as below.
numInvert[f_][y_?NumberQ] := Module[{x}, x /. FindRoot[y==f[x], {x,0}]]
For your example you could do
f[x_] = x+0.2*Sin[x]
Plot[numInvert[f][y], {y,0,1}]
Daniel Lichtblau
Wolfram Research
- References:
- inverse function computation
- From: "Margot" <gosia_sz@softhome.net>
- inverse function computation