# A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition

arXiv: https://arxiv.org/abs/1804.03415 · HTML: https://mlsanity.com/paper/1804.03415/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

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

- [Initialization Matters: Regularizing Manifold-informed Initialization for Neural Recommendation Systems](https://mlsanity.com/paper/2106.04993/) (2021)

## Abstract (arXiv)

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition components by integrating the multiresolution framework into the Implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm.