 
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(n 2 ), 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 log 2
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
Let M = [ jk ] # C
