@article{ABBCS-A-Stable-Polynomial-Time-Algorithm-For-The-Eigenpair-Problem,
Title = {A stable, polynomial-time algorithm for the eigenpair problem},
Author = {Diego Armentano and Carlos Beltr\´an and Peter B\"urgisser and Felipe Cucker and Michael Shub},
Pages = {1375--1437},
Year = {2018},
Doi = {10.4171/JEMS/789},
Journal = {Journal of the European Mathematical Society (JEMS)},
Volume = {20},
Number = {6},
Month = {04},
Note = {To appear in Journal of the European Mathematical Society.},
Abstract = {We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n \times n$ matrix $A$. 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.},
Url = {http://arxiv.org/abs/1505.03290},
Url2 = {http://dx.doi.org/10.4171/JEMS/789}
}