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We describe algorithms for computing eigenpairs (eigenvalue--eigenvector) ofa complex $n\times n$ matrix $A$. These algorithms are numerically stable,strongly accurate, and theoretically efficient (i.e., polynomial-time). We donot believe they outperform in practice the algorithms currently used for thiscomputational problem. The merit of our paper is to give a positive answer to along-standing open problem in numerical linear algebra.

A stable, polynomial-time algorithm for the eigenpair problem