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Numerical Experiments with Toeplitz Matrix Approximation Methods

Summary: Numerical Experiments with Toeplitz Matrix
Approximation Methods
Suliman Al-Homidan
January 16, 2005
Positive semidefinite Toeplitz matrix constraints arise naturally in
a variety of problems in engineering. This paper deals with the nu-
merical of this problem. Our approach is based on (i) interior point
primal-dual path-following method; (ii) a projection algorithm which
converges globally but slowly; (iii) the filterSQP method which is
faster. Hybrid methods that attempt to combine the best features
of both methods are then considered. Comparative numerical results
are reported.
Key words : Alternating projections, filterSQP method, non-smooth op-
timization, positive semidefinite matrix, primal-dual interior-point method,
Toeplitz matrix.
AMS (MOS) subject classifications; 65F99, 99C25, 65F30.
1 Introduction
The problem we are interested in is the best approximation of a given ma-
trix by a positive semidefinite symmetric Toeplitz matrix. Toeplitz matri-


Source: Al-Homidan, Suliman - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics