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arXiv · 1505.03290

A stable, polynomial-time algorithm for the eigenpair problem

Diego Armentano·Carlos Beltrán·Peter Bürgisser·Felipe Cucker·Michael Shub
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Abstract

We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ 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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Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker, Michael Shub. 2015-05-13. A stable, polynomial-time algorithm for the eigenpair problem. https://arxiv.org/abs/1505.03290

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