Isospectral Flows and Abstract Matrix Factorizations
Isospectral Flows and Abstract Matrix Factorizations
复制标题
等谱流和抽象矩阵分解
DOI：
10.1137/0725080
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发表时间：
1988
影响因子：
2.9
通讯作者：
L. K. Norris
中科院分区：
文献类型：
--
作者：
M. Chu;L. K. Norris
提出了在 n × n 矩阵的空间 $\operatorname{gl}(n)$ 中构建等谱流的通用框架。根据 $\operatorname{gl}(n)$ 的分割方式，该框架产生了不同类型的抽象矩阵分解。当以整数次采样时，这些流自然地定义了特殊的迭代过程，并且每个流与相应的抽象因式分解生成的序列相关联。所提出的理论将数值线性代数中使用的众所周知的矩阵分解技术统一为特殊情况，并且可能为一般矩阵分解问题提供更广泛的方法。
A general framework for constructing isospectral flows in the space $\operatorname{gl}(n)$ of n by n matrices is proposed. Depending upon how $\operatorname{gl}(n)$ is split, this framework gives rise to different types of abstract matrix factorizations. When sampled at integer times, these flows naturally define special iterative processes, and each flow is associated with the sequence generated by the corresponding abstract factorization. The proposed theory unifies as special cases the well-known matrix decomposition techniques used in numerical linear algebra and is likely to offer a broader approach to the general matrix factorization problem.