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On minimal Gerschgorin sets for families of norms

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Summary

In this note, the minimal Gerschgorin setG is defined for a matrixA, relative to a matrixD and a familyF of norms. This minimal Gerschgorin set is shown to be an inclusion region for the eigenvalues of a related collection\(\widehat\Omega \) of matrices, i.e.,

$$\sigma (\widehat\Omega ) \subseteq G.$$

The main result is a necessary and sufficient condition for equality to hold in the above inclusion. In addition, examples are given, one for which equality does not hold in the above inclusion.

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References

  1. Kovarik, Z. V.: Spectrum localization for certain classes of operators acting on C-spaces. To appear.

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Authors and Affiliations

  1. Department of Mathematics, Kent State University, 44242, Kent, Ohio, U.S.A.

    Richard S. Varga

  2. Department of Mathematics, Colorado State University, 80521, Fort Collins, Colorado, U.S.A.

    Bernard W. Levinger

Authors
  1. Richard S. Varga
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  2. Bernard W. Levinger
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Additional information

Research supported in part by the Atomic Energy Commission under Grant AT (11-1)-2075.

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Varga, R.S., Levinger, B.W. On minimal Gerschgorin sets for families of norms. Numer. Math. 20, 252–256 (1973). https://doi.org/10.1007/BF01436567

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  • DOI: https://doi.org/10.1007/BF01436567

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