A stable, polynomial-time algorithm for the eigenpair problem
Diego Armentano
Universidad de la República, Montevideo, UruguayCarlos Beltrán
Universidad de Cantabria, Santander, SpainPeter Bürgisser
Technische Universität Berlin, GermanyFelipe Cucker
City University of Hong Kong, Kowloon Tong, Hong KongMichael Shub
City University of New York, USA
Abstract
We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex matrix . 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.
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Cite this article
Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker, Michael Shub, A stable, polynomial-time algorithm for the eigenpair problem. J. Eur. Math. Soc. 20 (2018), no. 6, pp. 1375–1437
DOI 10.4171/JEMS/789