Alternating Projection Algorithm for Toeplitz Matrix
Department of Mathematical Sciences, King Fahd University of Petroleum and
Minerals, Dhahran 31261, PO Box 119, Saudi Arabia
Alternating projection onto convex sets is powerful tool for signal and image
restoration. The extensions of von Neumann's  alternating projection method
by Dykstra and Han [1, 2] permit the computation of proximity projection onto
certain convex sets. This paper exploits this fact in constructing a globally con-
vergent method for computing the closest positive definite symmetric Toeplitz
matrix to a specified matrix. Some applications to signal processing and control
problems are discussed. Comparative numerical results are also reported.
Key words : Alternating projections, least distance functions, non-smooth optimiza-
tion, positive semi-definite matrix, Toeplitz matrix.
AMS (MOS) subject classifications 65F99, 99C25, 65F30
 Dykstra, R. L. . An algorithm for restricted least squares regression, J.
Amer. Stat. Assoc. 78, pp. 839842.