RIA: The Canonical Correlations: Numerical Algorithms and Extensions

本研究的目的是进行结构化(如Toeplitz)矩阵偶的分析，并通过构造有效的预条件算子来分析数值算法连接的收敛行为。开发了当数据点被添加或删除时与典型关联相关的更新和更新问题的数值算法。对典型相关的下列扩展提出了理论和算法：具有一般双线性形式的典型相关、具有线性等式约束的典型相关、多个数据集的典型相关。这项研究有望在矩阵分解、数值线性代数和统计计算中产生新的概念，并促进和进一步推广典型相关分析在一般科学界的使用。

The goal of this research is to carry out the analysis of structured (e.g.Toeplitz) matrix pairs and to analyze the convergence behavior of the numerical algorithm connection with constructing efficient preconditioners. Numerical algorithms are developed for updating and downdating problems associated with canonical correlations when data points are added or deleted. Theories and algorithms are developed for the following extensions of canonical correlations: canonical correlations with a general bilinear form, canonical correlations with linear equality constraints, canonical correlations of several data sets. This research is expected to yield new concepts in matrix decompositions and numerical linear algebra and statistical computation, and facilitate and further spread the use of canonical correlation analysis in the general scientific community.