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一类特征值反问题(IEP)的基于矩阵方程的Ulm型算法

王艺宏, 李耀堂   

  1. 云南大学数学与统计学院, 昆明 650091
  • 收稿日期:2020-01-18 出版日期:2021-11-14 发布日期:2021-11-12
  • 基金资助:
    国家自然科学基金(11861077)资助.

王艺宏, 李耀堂. 一类特征值反问题(IEP)的基于矩阵方程的Ulm型算法[J]. 计算数学, 2021, 43(4): 444-456.

Wang Yihong, Li Yaotang. A ULM-TYPE ALGORITHM BASED ON MATRIX EQUATION FOR A CLASS OF INVERSE EIGENVALUE PROBLEMS (IEP)[J]. Mathematica Numerica Sinica, 2021, 43(4): 444-456.

A ULM-TYPE ALGORITHM BASED ON MATRIX EQUATION FOR A CLASS OF INVERSE EIGENVALUE PROBLEMS (IEP)

Wang Yihong, Li Yaotang   

  1. School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
  • Received:2020-01-18 Online:2021-11-14 Published:2021-11-12
应用求解算子方程的Ulm方法构造了求解一类矩阵特征值反问题(IEP)的新算法.所给算法避免了文献[Aishima K.,A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems,Linear Algebra and its Applications,2018,542:310-33]中算法在每次迭代中要求解一个线性方程组的不足,证明了在给定谱数据互不相同的条件下所给算法具有根收敛意义下的二次收敛性.数值实验表明本文所给算法在矩阵阶数较大时计算效果优于上文所给算法.
A new algorithm for solving a class of inverse eigenvalue problems of matrices is constructed by using the Ulm method for solving operator equations. The algorithm avoids the shortcomings of solving a system of linear equations in each iteration of the algorithm in[Aishima K., A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems, Linear Algebra and its Applications, 2018, 542:310-333], and it is proved that under the condition that the given spectrum data are different from each other, the algorithm has the quadratic convergence in the sense of root convergence. Numerical experiments show that the algorithm in this paper is better than the algorithm above when the matrix order is large.

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