Least squares Toeplitz matrix solutions of the matrix equation
Yongxin Yuan, Wenhua Zhao, Hao Liu · Linear and Multilinear Algebra · 2016
Let and we first solve the minimum Frobenius norm residual problem (Problem LSP): with unknown Toeplitz matrices X and Y. We then consider a best approximation problem: given Toeplitz matrices and , find such that where is the solution set of Problem LSP. We show that the best approximation solution is unique and derive an explicit formula for it.