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    • An affine eigenvalue problem on the nonnegative orthantPeer reviewedClosed access 

      2005, Blondel, Vincent; Ninove, Laure; Van Dooren, Paul, HE Léonard de Vinci
      Article scientifique
      In this paper, we consider the conditional affine eigenvalue problem where A is an n × n nonnegative matrix, b a nonnegative vector, and ∥·∥ a monotone vector norm. Under suitable hypotheses, we prove the existence and uniqueness of the solution (λ∗, x∗) and give its expression as the Perron root and vector of a matrix , where c∗ has a maximizing property depending on the considered norm. The equation ...

    • Affine iterations on nonnegative vectorsPeer reviewedClosed access 

      2004, Blondel, Vincent; NINOVE, Laure; Van Dooren, Paul, HE Louvain en Hainaut
      Article scientifique
      In this paper we consider three different iterations and and analyze their fixed points and ate of convergence. The initial vector x0 is positive, and the vectors b and y and the iteration matrix A are all nonnegative.