Alternating projection method for doubly stochastic inverse eigenvalue problems with partial eigendata

In this paper, we consider doubly stochastic inverse eigenvalue problems with partial eigendata, which aims to construct a doubly stochastic matrix from the prescribed partial eigendata. We propose the alternating projection method for two closed convex sets to solve the doubly stochastic inverse eigenvalue problems. And each subproblem in the alternating projection method can be solved easily. Under the assumption that the intersection of the two closed convex sets is not empty, the convergence of the alternating projection method is proved. Numerical results illustrate the effectiveness of our method.