A Global Solution for the Structured Total Least Squares Problem with Block Circulant Matrices

We study the Structured Total Least Squares (STLS) problem of system of linear equations Ax = b, where A has a block circulant structure with N blocks. We show that by applying the Discrete Fourier Transform (DFT), the STLS problem decomposes into N unstructured Total Least Squares (TLS) problems. The N solutions of these problems are then assembled to generate the optimal global solution of the STLS problem. Similar results are obtained for elementary block circulant matrices. Here the optimal solution is obtained by assembling two solutions: one of an unstructured TLS problem and the second of a multidimensional TLS problem. ∗MINERVA Optimization Center, Department of Industrial Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel. E-mail: {morbt@ie,becka@tx}.technion.ac.il. The research was partially supported by BSF grant #2002038