 
Summary: Classical Foundations of Algorithms for Solving
Positive Definite Toeplitz Equations \Lambda
Gregory S. Ammar y
Abstract
The ongoing development and analysis of efficient algorithms for solv
ing 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 math
ematics 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 pro
vide 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.
1 Introduction
Problems related to solving the system of equations Mx = b, where
M = Mn =
2
6 6 6 6 6 6 6 4
