** Next:** Introduction

# Classical Foundations of Algorithms for Solving Positive Definite
Toeplitz Equations

**Gregory S. Ammar**

### Abstract:

*The ongoing development and analysis of
efficient algorithms for
solving positive definite Toeplitz equations is motivated to a large
extent by the importance of these equations in signal processing
applications.
The role of positive definite Toeplitz matrices in this and other
areas of mathematics and engineering stems from
Schur's study of bounded analytic functions on the unit disk, and
Szego's theory of polynomials orthogonal on the unit circle.
These ideas underlie several Toeplitz solvers, and provide a
useful framework for understanding the relationships among these
algorithms.
In this paper we give an overview of several direct algorithms for
solving positive definite Toeplitz systems of linear equations
from this classical viewpoint.
*

*Greg Ammar *

Thu Sep 18 20:40:30 CDT 1997