一类特征值反问题(IEP)的基于矩阵方程的Ulm型算法

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

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 inAishima 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.