Armentano, DiegoBeltrán, CarlosBürgisser, PeterCucker, FelipeShub, Michael2019-01-312019-01-3120181435-9855https://depositonce.tu-berlin.de/handle/11303/9050http://dx.doi.org/10.14279/depositonce-8151Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex n×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.en510 MathematikEigenvalue computations, homotopy methodsArticle1435-9863