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A stable, polynomial-time algorithm for the eigenpair problem
Citation key ABBCS-A-Stable-Polynomial-Time-Algorithm-For-The-Eigenpair-Problem
Author Diego Armentano and Carlos Beltrán and Peter Bürgisser 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 $n × n$ 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.
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