Topological approach to diagonalization algorithms
Algebraic Topology
2022-04-14 v1 Combinatorics
Dynamical Systems
K-Theory and Homology
Abstract
In this paper we prove that there exists an asymptotical diagonalization algorithm for a class of sparse Hermitian (or real symmetric) matrices if and only if the matrices become Hessenberg matrices after some permutation of rows and columns. The proof is based on Morse theory, Roberts' theorem on indifference graphs, toric topology, and computer-based homological calculations.
Cite
@article{arxiv.2204.06111,
title = {Topological approach to diagonalization algorithms},
author = {Anton Ayzenberg and Konstantin Sorokin},
journal= {arXiv preprint arXiv:2204.06111},
year = {2022}
}
Comments
26 pages, 2 figures, 1 table