特征值反问题逼近解与极值化解的统一应用

The Unity and Application for Approximation and Extremal Solution of Inverse Eigenvalue Problems

基于矩阵最佳逼近与加权残值理论，本文把求解特征值反问题的矩阵逼近法和极值化方法统一为不同范数定义下的最小二乘问题。这对解决部分特征值和／或特征向量给足情况下的反问题提供了一个有效工具。结合工程实际，本文给出了具体应用的数值例子。

Based on matrix optimal approximation and weighted residuals theory, matrix approximation and extremal algorithm for resolving inverse eigenvalue problems are integrated with least squares problem under definition of different norms in this paper. It is a effective means for solving inverse problems of given partial eigenvalues and/or eigenvectors. Combining practice, a numerical example of engineering application is presented here.