Re: Solving a Toeplitz matrix equation

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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:
in stead of:

Hope this helps!!

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