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MathGroup Archive 2005

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Re: Composition of Expansions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55014] Re: Composition of Expansions
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Wed, 9 Mar 2005 06:34:40 -0500 (EST)
  • References: <d0jv47$n75$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Scott Guthery wrote:
> Bf[f_] := Sum[f[i/100]B[i,100,x],{i,0,100}]
> 
> gives the Bernstein expansion of f.
> 
> Df[f_] := 1-Bf[f]
> 
> is a function of interest.  I want to work with
> 
> Df[Df[Df[...[Df[g]]...]]] for some g[x_] := ...
> 
> i.e Bernstein expansions of Bernstein expansions.
> 
> As a simple example, suppose g[x_] := x^2 and try
> 
> Plot[Composition[Df, Df[g]], {x, 0, 1}]
> 
> Composition[Df, Df[g]] does not compute.
> 
> Thanks for any insight.
> 
> Cheers, Scott
> 
>  
> 
>  
> 
> <https://mail2.mobile-mind.com/exchange/sguthery/Drafts/RE:%20%20New%20in%205.1.1_x003F_.EML/#> 
> 
Hi,

Composition is an operation that takes two functions and returns a function:

h = Composition[f, g]

     Composition[f, g]

h[x]
	f[g[x]]

However, for repeated application of the same function, it is easier to 
use Nest:


Nest[f, x, 6]
       f[f[f[f[f[f[x]]]]]]

Regards,

David Bailey
dbaileyconsultancy.co.uk


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