Toeplitz Matrix Approximation
Department of Mathematical Sciences, King Fahd University of Petroleum and
Minerals, Dhahran 31261, PO Box 119, Saudi Arabia E-mail:
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 quasi-Newton 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, non-smooth optimiza-
tion, positive semi-definite matrix, Toeplitz matrix, quasi-Newton method.
The problem we are interested in, is the best approximation of a given matrix by a
positive semi-definite symmetric Toeplitz matrix. Toeplitz matrices appear naturally
in a variety of problems in engineering. Since positive semi-definite Toeplitz matrices
can be viewed as shift-invariant autocorrelation matrices, considerable attention has
been paid to them, especially in the areas of stochastic filtering and digital signal
processing applications  and . Several problems in digital signal processing