English

A stable, polynomial-time algorithm for the eigenpair problem

Numerical Analysis 2015-05-14 v1

Abstract

We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex n×nn\times n matrix AA. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not believe they outperform in practice the algorithms currently used for this computational problem. The merit of our paper is to give a positive answer to a long-standing open problem in numerical linear algebra.

Keywords

Cite

@article{arxiv.1505.03290,
  title  = {A stable, polynomial-time algorithm for the eigenpair problem},
  author = {Diego Armentano and Carlos Beltrán and Peter Bürgisser and Felipe Cucker and Michael Shub},
  journal= {arXiv preprint arXiv:1505.03290},
  year   = {2015}
}

Comments

69 pages. This paper resulted after merging the independent works arXiv:1410.0116 and arXiv:1410.2179. The present work contains considerably more refined results than the two predecessors

R2 v1 2026-06-22T09:33:18.154Z