Numerical Optimization for the Length Problem

Christos Kravvaritis () and Marilena Mitrouli ()
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Christos Kravvaritis: University of Athens
Marilena Mitrouli: University of Athens

Chapter Chapter 7 in Applications of Mathematics and Informatics in Military Science, 2012, pp 87-93 from Springer

Abstract: 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.

Keywords: Length problem; Normalized orthogonal matrices; Numerical optimization (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-4109-0_7

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