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

```

• Prev by Date: Re: help with mathematica
• Next by Date: findfit or solve?
• Previous by thread: Composition of Expansions
• Next by thread: Generating PDF figures with correct fonts in Mac OS X