RIA: The Canonical Correlations: Numerical Algorithms and Extensions

本研究的目的是对结构化（如toeplitz）矩阵对进行分析，并分析数值算法与构造有效预条件相关的收敛行为。当数据点被添加或删除时，数值算法被开发用于更新和降级与典型相关性相关的问题。理论和算法的发展为以下扩展的典型相关：典型相关与一般双线性形式，典型相关与线性等式约束，几个数据集的典型相关。本研究有望在矩阵分解、数值线性代数和统计计算方面产生新的概念，并促进典型相关分析在一般科学界的应用。

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.