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Composition of Expansions

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Mar 8, 2005, 5:34:47 AM3/8/05

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

unread,

Mar 9, 2005, 6:59:34 AM3/9/05

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,

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