Approximate Toeplitz Matrix Problem Using Semidefinite Programming |
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Authors: | S Al-Homidan |
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Institution: | (1) Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia |
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Abstract: | Given a data matrix, we find its nearest symmetric positive-semidefinite Toeplitz matrix. In this paper, we formulate the
problem as an optimization problem with a quadratic objective function and semidefinite constraints. In particular, instead
of solving the so-called normal equations, our algorithm eliminates the linear feasibility equations from the start to maintain
exact primal and dual feasibility during the course of the algorithm. Subsequently, the search direction is found using an
inexact Gauss-Newton method rather than a Newton method on a symmetrized system and is computed using a diagonal preconditioned
conjugate-gradient-type method. Computational results illustrate the robustness of the algorithm. |
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Keywords: | Primal-dual interior-point methods Projection methods Toeplitz matrices Semidefinite programming |
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