 
Summary: The Generalized Schur Algorithm for the Superfast
Solution of Toeplitz Systems
Gregory S. Ammar
Department of Mathematical Sciences
Northern Illinois University
DeKalb, Illinois 60115
William B. Gragg
Department of Mathematics
University of Kentucky
Lexington, Kentucky 40506
Abstract
We review the connections between fast, O(n2
), Toeplitz solvers
and the classical theory of Szego polynomials and Schur's algorithm.
We then give a concise classically motivated presentation of the su
perfast, O(n log2
2 n), Toeplitz solver that has recently been introduced
independently by deHoog and Musicus. In particular, we describe this
algorithm in terms of a generalization of Schur's classical algorithm.
1 Introduction
