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Diego Armentano (2013)

Complexity of Path-Following Methods for the Eigenvalue Problem

Foundation of Computational Mathematics, (submitted).

A unitarily invariant projective framework is introduced to analyze the complexity of path–following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill–posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s γ-Theorem is proven. The main result of this paper bounds the complexity of path–following methods in terms of the length of the path in the condition metric.
El .pdf se puede descargar desde mi página personal: www.cmat.edu.uy/~diego
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