Topological approach to diagonalization algorithms

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.

26 pages, 2 figures, 1 table