 
Summary: 1
Toeplitz Matrix Approximation
Suliman AlHomidan
Department of Mathematical Sciences, King Fahd University of Petroleum and
Minerals, Dhahran 31261, PO Box 119, Saudi Arabia Email:
homidan@kfupm.edu.sa
Abstract
This paper deals with numerical Toeplitz matrix approximation. Our ap
proach is based on (i) a projection algorithm which converges globally but
slowly; and (ii) the quasiNewton method which is faster. Hybrid methods that
attempt to combine the best features of both methods are then considered.
Key words : Alternating projections, least distance functions, nonsmooth optimiza
tion, positive semidefinite matrix, Toeplitz matrix, quasiNewton method.
1 Introduction
The problem we are interested in, is the best approximation of a given matrix by a
positive semidefinite symmetric Toeplitz matrix. Toeplitz matrices appear naturally
in a variety of problems in engineering. Since positive semidefinite Toeplitz matrices
can be viewed as shiftinvariant autocorrelation matrices, considerable attention has
been paid to them, especially in the areas of stochastic filtering and digital signal
processing applications [12] and [21]. Several problems in digital signal processing
