交替投影算法求解非负逆特征值问题

Alternating Projection Method for Solving Nonnegative Inverse Eigenvalue Problems

通过把给定部分特征对的非负逆特征值问题转化为一个凸可行性问题,提出交替投影算法求解该问题。建立了这一算法的线性收敛性。最后,通过数值例子,比较了交替投影算法和非光滑牛顿法(白等人2011年提出)的收敛效率。数值实验结果表明,交替投影算法总是能收敛到问题的解,而非光滑牛顿法在一些情形下求不出解。此外,交替投影算法收敛的效率也比非光滑牛顿法高。

The alternating projection method is proposed for solving nonnegative inverse eigenvalue prob-lems with partial eigendata, by reformulating the problem as a convex feasibility problem. The (linear) convergnece property of the method is established. At last, some numerical experiments are provided to compare the method with the non-smooth Newton algorithm proposed by Bai et al. in 2011. Numerical experiment results show that the alternative projection algorithm always converges to the solution of the problem, while the non-smooth Newton method fails to find the solution in some cases. In addition, the alternative projection algorithm is more efficient than the non-smooth Newton method.