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Diego Armentano and Felipe Cucker (2013)

A Randomized Homotopy for the Hermitian Eigenpair Problem

Foundation of Computational Mathematics, (submitted).

We describe and analyze a randomized homotopy algorithm for the Hermitian eigenvalue problem. Given an n × n Hermitian matrix A the algorithm returns, almost surely, a pair (λ, v) which approximates, in a very strong sense, an eigenpair of A. We prove that the expected cost of this algorithm, where the expectation is both over the random choices of the algorithm and a probability distribution on the input matrix A, is O(n^4 ), that is, quadratic on the input size. Our result relies on a cost assumption for some pseudo-random number generators whose rationale is argued by us.
Artículo sometido para publicación en Septiembre de 2013. El .pdf se puede descargar desde mi página personal: www.cmat.edu.uy/~diego
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