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A stable, polynomial-time algorithm for the eigenpair problem
Citation key BC-A-Stable-Polynomial-Time-Algorithm-For-The-Eigenpair-Problem
Author Peter Bürgisser and Felipe Cucker
Year 2014
Month 10
Note This preprint was merged in 2015 with arXiv:1410.2179 into arXiv:1505.03290.
Abstract We describe algorithms for computing eigenpairs (eigenvalue-eigenvector) 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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