**Volume 17, Issue 4, pp 477-487**

**Publication Date**: 2017-10-14

**Li-Jun Zhao**
- School of Mathematics and Information Engineering, Taizhou University, Linhai, Zhejiang, 317000, P. R. China

**Ru Huang**
- Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, USA

This article considers an inverse eigenvalue problem for centrosymmetric matrices under a central principal submatrix constraint and the corresponding optimal approximation problem. We first discuss the specified structure of centrosymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the inverse eigenvalue problem, and we derive an expression for its general solution. Finally, we obtain an expression for the solution to the corresponding optimal approximation problem.

Centrosymmetric matrix, central principal submatrix, inverse eigenvalue problem, optimal approximation problem

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