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Closest normal matrix finally found!

 3 years ago
source link: https://link.springer.com/article/10.1007/BF01937278
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Closest normal matrix finally found!

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Closest normal matrix finally found!

BIT Numerical Mathematics

volume 27, pages585–598(1987)Cite this article

Abstract

A method of finding the closest normal matrix in the Frobenius matrix norm is developed. It is shown that if a matrix is represented in those coordinates where its closest normal matrix is diagonal, its restriction to any pair of coordinate directions is a multiple of a real diagonal and skew nondiagonal 2×2 matrix. A convergent algorithm to bring an arbitrary matrix into that form is described and results of numerical tests are reported.

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Author information

Affiliations

  1. Department of Computer Science, Chalmers Institute of Technology and the University of Göteborg, S-41296, Göteborg, Sweden

    Axel Ruhe

Additional information

Dedicated to the memory of Peter Henrici (1923–1987).

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Ruhe, A. Closest normal matrix finally found!. BIT 27, 585–598 (1987). https://doi.org/10.1007/BF01937278

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Subject classifications

  • AMS(MOS)
  • 65F35
  • 15A60

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