Numerische Mathematik

, Volume 123, Issue 2, pp 309–331 | Cite as

Solving inverse cone-constrained eigenvalue problems



We compare various algorithms for constructing a matrix of order \(n\) whose Pareto spectrum contains a prescribed set \(\Lambda =\{\lambda _1,\ldots , \lambda _p\}\) of reals. In order to avoid overdetermination one assumes that \(p\) does not exceed \(n^2.\) The inverse Pareto eigenvalue problem under consideration is formulated as an underdetermined system of nonlinear equations. We also address the issue of computing Lorentz spectra and solving inverse Lorentz eigenvalue problems.

Mathematics Subject Classification

15A18 65F18 65H17 



The first author has been supported by Projet Fondecyt Nr. 1080173 (Chile) and “Programa de Financiamiento Basal” from the Center of Mathematical Modeling, Universidad de Chile. He thanks also the University of Avignon for the hospitality and working facilities offered during a visit at this institution.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.Department of MathematicsUniversity of AvignonAvignonFrance

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