中文摘要：

讨论实双反对称矩阵和实双对称矩阵的二次特征值反问题及其最佳逼近问题,利用矩阵的奇异值分解,建立了二次特征值反问题解的充要条件,并给出了其解集的一般表达式。进而考虑了其最佳逼近问题的存在性与唯一性,得到了最佳逼近解的表达式。

英文摘要：

The paper concerns the quadratic inverse eigenvalue problem of real double symmetric matrix and real double antisymmetric matrix and it＇ s optimal approximation problem. A necessary and sufficient condition for the solution of the quadratic inverse eigenvalue problem is constructed by singular value decomposition of matrix, the general expression of the solution to the problem is provided. Then the existence and uniqueness of the optimal approximation problem is discussed and the expression is provided for the optimal approximation problem.