Posted by Martijn van Beurden on June 19, 1998 at 05:54:29:

In Reply to: Re: Solving a Toeplitz matrix equation posted by Shilpa Singhal on February 05, 1998 at 14:14:11:

: : I have an equation of the form

: : h(i,j)=M(i,j,k,l)g(k,l)

: : where M is a symmetric semipositive definite block

: : Toeplitz matrix.

: : I need to either invert or solve for g iteratively in the

: : most efficient way possible. Can anyone suggest

: : a routine that they know of themselves or know of in the

: : NetLib repository (preferably in fortran).

: : I've heard of conjugate gradient and Levison algorithms, but

: : I can't find them

: : Many thanks

: Graham French

: The best way to find something like this at Netlib

: is to use Netlib search engine. When I entered in

: "Solving a Toeplitz matrix equation " and

: "Conjugate gradient and Levison algorithms" , I got quite

: a few hits'`, but I am unsure if any of the packages

: are suitable for your needs....

: Hope this helps !

Well, I didn't find anything on the web, but a student

here just programmed Trench's algorithm to invert a

Toeplitz matrix (it even works for symmetric complex

Toeplitz matrices!). You can find the algoritm in

Golub and Van Loan: Matrix Computations

However, don't program it right away, because there is

a small error in it (version 1996 p. 199).

The second line should state:

gamma=1/(1+r(1:n-1)y(1:n-1))

in stead of:

gamma=1/(1+r(1:n-1)y(n-1:-1:1))

Hope this helps!!