Toeplitz matrices

[Paul]

Toeplitz matrices arise all over the place.
In electromagnetic antenna calculations, the matrices are symmetric and complex - and large.
Fortunately, NxN components do not have to be stored, as the first row alone contains all elements.

Trench's algorithm can be used to invert such a matrix. In fact, the inverse only needs an N-element
vector to be calculated too, from which the actual inverse elements are easy to derivce on th fly as needed
as long as you want them in row order. Actually you get row 1 and row N (which is row 1 reversed) first,
then you get row 2 and row (n-1) etc.

In other applications the ,matrix is often Hermitian-symmetric Toeplitz. This also needs only the first
row to be stored, as other row elements are either equal or conjugates of these.

Does anybody know if such a matrix can be inverted by Trench's algorithm, i.e. by computing only
an N-element vector from which the rows of the inverse can then be simply derived on the fly as needed?

LAPACK seems to lack routines that specifcially take advantage of the fast methods available for Toeplitz matrices.