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:我们研究了逆向的乙基值问题,以找到带有特定乙基值的双重随机矩阵。我们利用Dykstra的算法和交替投影过程的结合,在非凝固器组中得出混合算法,以找到双重随机矩阵和配有规定的乙基值的对称二基随机矩阵。此外,我们证明也证明了拟议的算法趋同和线性趋同。我们提供了数字示例,以证明我们方法的效率。