Constructing Fast Approximate Eigenspaces With Application to the Fast Graph Fourier Transforms

We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The are factored into a fixed number fundamental components that can be efficiently manipulated (we consider extended orthogonal Givens or scaling shear transformations). these controls the trade-off between approximation accuracy computational complexity projecting on eigenspaces. write minimization problems for single provide closed-form solutions. Then we propose algorithms iterative update all until convergence. show results random matrices an application graph Fourier transforms directed undirected graphs.