We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider extended orthogonal Givens or scaling and shear transformations). The number of these components controls the trade-off between approximation accuracy and the computational complexity of projecting on the eigenspaces. We write minimization problems for the single fundamental components and provide closed-form solutions. Then we propose algorithms that iterative update all these components until convergence. We show results on random matrices and an application on the approximation of graph Fourier transforms for directed and undirected graphs.
翻译:我们调查与对称矩阵和一般矩阵相关的电子空间数字效率近似值。 将电子空间纳入固定数量的基本组成部分中, 以便有效操作( 我们考虑扩展正方形视图或缩放和剪切转换)。 这些组成部分的数量可以控制对准精确度和对正方形空间投影的计算复杂性之间的权衡。 我们为单个基本组成部分写最小化问题并提供封闭式解决方案。 然后我们提出迭代更新所有这些组成部分直至趋同的算法。 我们用随机矩阵和图四ier变形近似图的应用程序显示结果, 用于定向和非定向图。