Studies on Matrix Completion and Partial Realization with Nuclear Norm Minimization
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The field of Compressed Sensing addresses the problem of recovering relatively sparse entities from a limited number of data points. Low rank matrices arise in a wide range of settings in this field and two of its applications, Matrix Completion and Partial Realization, have been studied and analyzed in this thesis by the method of nuclear norm minimization. The method of alternating directions for nuclear norm minimization was applied to solve the matrix completion problem and the obtained MATLAB results were analyzed. The partial realization problem, which is a control systems application, was solved through the compressed sensing approach and a convex optimization package, and CVX was used to implement it on low order matrices. Computations were performed on different stable systems and the obtained results were presented and explained.