Submatrix constrained left and right inverse eigenvalue problem for centrosymmetric matrices

ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix constraint, where is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) satisfying the matrix constraint, where A and are both centrosymmetric matrices. Using the similar structure of A and , we discuss the sufficient and necessary conditions for the left and right inverse eigenvalue problem having solutions, and give the expression for its general solution. Then, we discuss its optimal approximation problem and gain the expression of its solution. Last, we provide a feasible algorithm for computing the unique solution to its optimal approximation problem, which is proved by some numerical examples.