双中心矩阵反问题及其在电网络理论中的应用

The Inverse Problem of Doubly Center Matrices and Its Application to the Theory of Electric Network

本文研究双中心矩阵反问题。建立了双中心矩阵反问题的最小二乘解,得到了解的具体表达式。讨论了用双中心矩阵反问题的解构造给定矩阵的最佳逼近问题,给出该问题有解的充分必要条件和解的表达式。设计了相应的算法并给出了其在电网络理论中的应用。

This paper is focused on the inverse problem of doubly center matrices. The least-square solutions to the inverse problem are established and their general form is given. Based on the solution set, the optimal approximation to a given matrix is constructed, and the necessary and sufficient conditions for the solvability of the problem are given and the expression for the solution is provided. The corresponding algorithms are proposed and applications to the theory of electric network are illustrated by examples.