带子矩阵约束的二次逆特征值问题的最小二乘埃尔米特广义斜哈密顿矩阵迭代解

The least squares solutions of quadratic inverse eigenvalue problems with Hermitian and generalized Hamiltonian matrix under submatrix constraints

针对带子矩阵约束的二次逆特征值问题的最小二乘埃尔米特广义斜哈密顿结构矩阵解问题,给出了一种共枙梯度迭代算法。首先提出了带子矩阵约束的二次逆特征值问题的最小二乘问题及其最佳逼近问题;然后分别给出了基于共轭梯度的迭代算法,证明了算法的收敛性。对于任意初始约束矩阵,在不存在舍入误差的情况下,用该迭代算法可以在有限步迭代中得到迭代解。最后,给出了一个数值实例,数值实例证明了所提算法的有效性。

An iterative algorithm for the solution of the quadratic inverse eigenvalue problem of band matrix constraint is proposed based on the least-squares Hermite generalized oblique Hamiltonian structure matrix.Firstly,the least squares problem and its optimal approximation problem for quadratic inverse eigenvalue problems with band matrix constraints are presented.Then the iterative algorithm based on conjugate gradient is given and the convergence of the algorithm is proved.For any initial constraint matrix,the iterative algorithm can obtain the iterative solution in finite step iteration without rounding error.Finally,a numerical example is given to demonstrate the effectiveness of the proposed algorithm.