求解对称非负逆特征值问题的一阶黎曼算法  

Riemannian Algorithms of Order One for Solving Symmetric Nonnegative Inverse Eigenvalue Problems

作　　者：吕文平 王湘美 

机构地区：[1]贵州大学数学与统计学院,贵州 贵阳

出　　处：《应用数学进展》2022年第10期7411-7421,共11页Advances in Applied Mathematics

摘　　要：基于对称非负逆特征值问题的黎曼优化模型,提出了求解该问题的黎曼梯度下降算法和黎曼共轭梯度算法,并分析了这两种算法的收敛性。通过数值实验,比较了两种算法的收敛效率。数值结果表明,求解高阶的非负逆特征值问题时,黎曼共轭梯度算法的收敛效率要高于黎曼梯度下降算法。The Riemannian gradient descent algorithm and the Riemannian conjugate gradient algorithm are proposed for solving the symmetric nonnegative inverse eigenvalue problems, respectively, to-gether with the convergence analysis. At last, some numerical experiments are provided to illus-trate the convergence of the algorithms, and they show that the Riemannian conjugate gradient al-gorithm is more effective than the Riemannian gradient descent algorithm.

关 键 词：对称非负逆特征值问题 黎曼梯度下降算法 黎曼共轭梯度算法 收敛性 

分 类 号：O186.12[理学—数学]