非负矩阵特征值反问题的研究进展

Study progress of inverse eigenalue problems for nonnegative matrices

本文简单介绍一下矩阵特征值反问题的应用背景,简要综述自20世纪40年代以来非负矩阵特征值反问题的解的存在性理论和算法方面的一些研究进展,偏重作者在黎曼优化算法方面的一点研究工作.最后,给出这方面今后的发展方向.

The importance of inverse eigenvalue problems is briefly presented.Some existence-related results and numerical methods for inverse eigenvalue problems for nonnegative matrices,published since the 1940s,are reviewed.These reviews somewhat stress the author s work in Riemannian optimization methods.Further study trends are also mentioned.