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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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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. 1375–1437DOI 10.4171/JEMS/789