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.

翻译：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。通过结合Dykstra算法与非凸集上的交替投影过程，我们提出了混合算法，用于构造具有指定特征值的双随机矩阵和对称双随机矩阵。此外，我们证明了所提算法的收敛性，并进一步证明了线性收敛性。数值算例验证了该方法的高效性。