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Numerical Optimization for the Length Problem

In: Applications of Mathematics and Informatics in Military Science

Author

Listed:
  • Christos Kravvaritis

    (University of Athens)

  • Marilena Mitrouli

    (University of Athens)

Abstract

The length problem for normalized orthogonal (NO) matrices (satisfying $$A{A}^{T} = {A}^{T}A = c(A){I}_{n}$$ , for some constant c(A)), which is the determination of c(n)=sup{c(A)|A∈ℝ n ×n , NO matrix}, is formulated as a constrained optimization problem. The most appropriate numerical optimization technique for its study is analyzed. The corresponding numerical results provide useful experimental evidence concerning the possible values of c(n) for various values of n and the relevant significance of Hadamard and weighing matrices is pointed out.

Suggested Citation

  • Christos Kravvaritis & Marilena Mitrouli, 2012. "Numerical Optimization for the Length Problem," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Military Science, edition 127, chapter 0, pages 87-93, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-4109-0_7
    DOI: 10.1007/978-1-4614-4109-0_7
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