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Applying the iteration methods to simpler functions
You are confusing Bell matrices and Carleman matrices again. The (generalized) Bell matrix of is

whereas the Carleman matrix (is

all the other stuff is right, though, and interesting. I like your notation, but I'm having trouble following your series notation.

I think the example of is an interesting one, and I intend on looking into it, but first for the purposes of illustration, your simplest example is the nicest, for example, addition . Taking the Bell matrix:

and subtracting the identity matrix:

gives a non-invertible matrix, so doing the choppy thing gives:

putting this in the matrix equation gives:

and since the matrix is invertible now, we can multiply both sides by its inverse:

This gives the natural Abel function (choosing the constant term to be zero) which satisfies the equation .

I like that example Smile I know you already talked about it, but I wanted to show a matrix-based way of doing the chopping process.

So in general, the matrix equation would give the coefficients of the natural Abel function of f.

Andrew Robbins

Messages In This Thread
RE: Applying the iteration methods to simpler functions - by andydude - 11/12/2007, 09:40 AM

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