Least-Squares Solutions of Inverse Problems for r-Circulant Matrices

摘要

The least-square solutions of inverse problems for the r -circulant matrices are considered and a general expression of such a matrix is presented. Moreover, for the special case of the least-square problems, the necessary and sufficient conditions for the solvability and the general solution of these problems are given. Then the optimal approximation problem for the r -circulant matrix inverse problem is discussed. The existence and the uniqueness of this matrix are proved and the expression of this unique matrix is presented. We also give two numerical examples to support the theory established in this paper.