Low-Rank Approximation of Circulant Matrix to a Noisy Matrix

This paper constructs structured circulant positive semi-definite matrix that is nearest to a given data matrix. The problem arises in various applications since the matrix formed from the data collected does not maintain either the desirable rank or specified structure as is expected. The objective is to recover original matrix while maintaining the physical structure. Some of the numerical issues involved will be addressed including unsymmetrical of the problem. We presented new methods to determine approximation of optimal matrices. Comparative numerical results are also reported.