Geodesic
A stable, polynomial-time algorithm for the eigenpair problem
Journal of the European Mathematical Society, Tome 20 (2018) no. 6, pp. 1375-1437

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/789
Classification : 65-XX, 15-XX
Keywords: Eigenvalue computations, homotopy methods 
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     title = {A stable, polynomial-time algorithm for the eigenpair problem},
     journal = {Journal of the European Mathematical Society},
     pages = {1375--1437},
     publisher = {mathdoc},
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Diego Armentano; Carlos Beltrán; Peter Bürgisser; Felipe Cucker; Michael Shub. A stable, polynomial-time algorithm for the eigenpair problem. Journal of the European Mathematical Society, Tome 20 (2018) no. 6, pp. 1375-1437. doi: 10.4171/jems/789

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