非正交一般联合块对角化问题的代数方法
An Algebraic Approach to Non-Orthogonal General Joint Block Diagonalization
AI总结：
本文提出通过求解线性方程组和相似变换实现非正交一般联合块对角化问题的解，并给出精确解的充分必要条件及数值方法。
摘要：
本文提出通过求解线性方程组和相似变换实现非正交一般联合块对角化问题的解，并给出精确解的充分必要条件及数值方法。
英文摘要：
The exact/approximate non-orthogonal general joint block diagonalization ({\sc nogjbd}) problem of a given real matrix set $\mathcal{A}=\{A_i\}_{i=1}^m$ is to find a nonsingular matrix $W\in\mathbb{R}^{n\times n}$ (diagonalizer) such that $W^T A_i W$ for $i=1,2,\dots, m$ are all exactly/approximately block diagonal matrices with the same diagonal block structure and with as many diagonal blocks as possible. In this paper, we show that a solution to the exact/approximate {\sc nogjbd} problem can be obtained by finding the exact/approximate solutions to the system of linear equations $A_iZ=Z^TA_i$ for $i=1,\dots, m$, followed by a block diagonalization of $Z$ via similarity transformation. A necessary and sufficient condition for the equivalence of the solutions to the exact {\sc nogjbd} problem is established. Two numerical methods are proposed to solve the {\sc nogjbd} problem, and numerical examples are presented to show the merits of the proposed methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
