A stable, polynomial-time algorithm for the eigenpair problem

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.

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