# Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms

arXiv: https://arxiv.org/abs/2002.09723 · HTML: https://mlsanity.com/paper/2002.09723/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [An iterative coordinate descent algorithm to compute sparse low-rank approximations](https://mlsanity.com/paper/2107.14608/) (2021)

## Abstract (arXiv)

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.