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Optimization related question on Toeplitz matrix

Posted 10 years ago


I would like to find a complex symmetric Toeplitz matrix C (one could do any iterative method) from (huge) set of the data { y }, where every complex-scalar y can be described by a following model which includes the matrix C (whose size is say M x M),

y = 1^T C X C^H 1,

where 1 is a column vector of ones, and matrix X (size M x M) is perfectly known. (.)^T and (.)^H denotes the transpose and Hermitian operator. So, only unknown is matrix C.

My questions are: (1) is the solution of this problem really feasible ? On the other hand, if 1^T and 1 do not exist in the above model, then the received data y would be a matrix. And the solution of this problem can be obtained as mentioned in the attached reference (see section D for instance of the reference). (2) if yes, then I would greatly appreciate the solution for this problem or any pointer to solve this question. (3) if no, then please provide the reasoning.

Many thanks in advance for your time and reading this question, \Shashi

POSTED BY: Shashi Kant
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