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Numerical procedure for solving a minimization eigenvalue problem

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Summary

A numerical procedure for solving the left eigenvalue problem

$$\lambda + L(k) = \min _j [L(j) + K(j,k)],$$

and its right counterpart, is described;K is a (known) realn×n matrix. The first stage uses a modification of the Karp and von Golitschek procedure for finding the minimum cyclic average λ ofK along with a minimizing cycle. The second stage employs this information to generateL, by a very similar algorithm.

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Author notes

  1. Luis M. Floria

    Present address: Instituto de Ciencas de los Materiales de Aragón, CSIC-Universidad de Zaragoza, E-50015, Zaragoza, Spain

Authors and Affiliations

  1. Department of Physics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    Luis M. Floria

  2. Institute for Theoretical Physics, University of California at Santa Barbara, 93106, Santa Barbara, CA, USA

    Robert B. Griffiths

Authors
  1. Luis M. Floria
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  2. Robert B. Griffiths
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Floria, L.M., Griffiths, R.B. Numerical procedure for solving a minimization eigenvalue problem. Numer. Math. 55, 565–574 (1989). https://doi.org/10.1007/BF01398916

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  • DOI: https://doi.org/10.1007/BF01398916

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