Applying the iteration methods to simpler functions

[bo198214]

You are confusing Bell matrices and Carleman matrices again.

No, I consistently swapped them till now!

So for everyone the correct usage: The \( n \)-th row of the Carleman matrix contains the coefficients of the \( n \)-th power of the power series. The \( n \)-th column of the Bell matrix contains the coefficients of the \( n \)-th power of the power series. The Bell and Carleman matrix are transposed to each other.

doing the choppy thing gives:
\( \mathbf{C}(\mathbf{B}_x[x + d] - \mathbf{I})\mathbf{D}= \left[\begin{tabular}{ccc}
1 & 0& 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0
\end{tabular}\right]\left[\begin{tabular}{ccc}
0 & d & d^2 & d^3 \\
0 & 0 & 2d & 3d^2 \\
0 & 0 & 0 & 3d \\
0 & 0 & 0 & 0
\end{tabular}\right]\left[\begin{tabular}{ccc}
0 & 0 & 0 \\
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{tabular}\right] = \left[\begin{tabular}{ccc}
d & d^2 & d^3 \\
0 & 2d & 3d^2 \\
0 & 0 & 3d
\end{tabular}\right] \)
...
I wanted to show a matrix-based way of doing the chopping process.

Thanks for this.