论文标题
关于具有规定特征值的双随机矩阵的数值结构
On a numerical construction of doubly stochastic matrices with prescribed eigenvalues
论文作者
论文摘要
我们研究了具有指定特征值的双随机矩阵的逆特征值问题。通过利用Dykstra算法和在非凸组集合上的交替投影过程的组合，我们得出了混合算法，用于查找带有规定的特征元素的双随机矩阵和对称双重随机矩阵。此外，我们证明了所提出的算法收敛并证明了线性收敛。提出了数值示例以证明我们方法的效率。
We study the inverse eigenvalue problem for finding doubly stochastic matrices with specified eigenvalues. By making use of a combination of Dykstra's algorithm and an alternating projection process onto a non-convex set, we derive hybrid algorithms for finding doubly stochastic matrices and symmetric doubly stochastic matrices with prescribed eigenvalues. Furthermore, we prove that the proposed algorithms converge and linear convergence is also proved. Numerical examples are presented to demonstrate the efficiency of our method.
