We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended orthogonal Givens transformations, including Givens rotations as a special case. We propose an efficient greedy algorithm to solve such a problem and show that it strikes a balance between approximation accuracy and speed of computation. The approach is relevant to spectral methods and we illustrate its application to PCA.
翻译:我们研究近似正方位矩阵的问题,以便其应用在数字上既快又准确。我们通过解决一系列结构化矩阵的优化问题找到近似值,我们称之为扩展正方位变量转换,包括作为特例的Genes旋转。我们建议一种高效的贪婪算法来解决这样一个问题,并表明它在近方精确度和计算速度之间取得了平衡。这种方法与光谱方法相关,并演示其对五氯苯甲醚的应用。