An incremental method to compute (Abel) matrix inverses

[bo198214]

what is an abel matrix ?

i know carleman and bell matrix ... whats the difference ?

maybe its the matrix equivalent of the infinite linear equations of andrews slog ...

Oh the term was introduced by Andrew and indeed is the matrix equivalent of the infinite equation system of Andrew's slog.

Its C-I transposed (C is the infinite Carleman matrix, I the infinite identity matrix) and first column removed (which consists of only 0's) and then square truncated according to your needs of precision.

But the above inversion formula does not depend on A being an Abel matrix. It works for every invertible matrix.
But currently I see that the internal inversion algorithms of Sage are even faster to recompute the whole inverse than doing an incremtal inverse with the above formula *sigh*