SQP Algorithms for Solving Toeplitz Matrix
Department of Mathematical Sciences, King Fahd University of Petroleum and
Minerals, Dhahran 31261, PO Box 119, Saudi Arabia E-mail:
Given an n×n matrix F, we find the nearest symmetric positive semi-definite
Toeplitz matrix T to F. The problem is formulated as a nonlinear minimization
problem with positive semi-definite Toeplitz matrix as constraints. Then a
computational framework is given. An algorithm with rapid convergence is
obtained by l1Sequential Quadratic Programming (SQP) method.
Key words : non-smooth optimization, positive semi-definite matrix, Toeplitz ma-
trix, SQP method, l1SQP Method.
AMS (MOS) subject classifications 65F99, 99C25, 65F30
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