基于商奇异值分解的一类二次特征值反问题

摘要

讨论二次特征值反问题在主子阵约束下广义反自反解及其最佳逼近问题。利用矩阵的奇异值分解和商奇异值分解，建立了在主子阵约束下广义反自反矩阵解的充要条件，并给出了其通解的表达式。进而考虑了其最佳逼近问题解的存在性与唯一性，得到了最佳逼近解的表达式。%In this paper,we discuss the inverse quadratic eigenvalue problem in a submatrix constraint generalized antireflexive solutions and its optimal approximation problem. Using the singular value decomposition ( SVD) and the quotient singular value decomposition(QSVD) of a matrix and matrix pair,the authors established the necessary and sufficient conditions for the existence of the generalized antireflexive solutions and the expressions for the in-verse quadratic eigenvalue problem of a matrix under a submatrix constraint. Then we consider the existence and u-niqueness of the optimal approximation problem solutions and obtain the expression for the optimal approximation solution.