D-optimal designs embedded in Hadamard matrices and their effect on the pivot patterns |
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Authors: | M Mitrouli |
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Institution: | Department of Mathematics, University of Athens, Panepistemiopolis 15784, Athens, Greece |
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Abstract: | In this paper we develop a new approach for detecting if specific D-optimal designs exist embedded in Sylvester-Hadamard matrices. Specifically, we investigate the existence of the D-optimal designs of orders 5, 6, 7 and 8. The problem is motivated to explaining why specific values appear as pivot elements when Gaussian elimination with complete pivoting is applied to Hadamard matrices. Using this method and a complete search algorithm we explain, for the first time, the appearance of concrete pivot values for equivalence classes of Hadamard matrices of orders n = 12, 16 and 20. |
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Keywords: | Primary 65F40 65F05 15A15 Secondary 05B20 |
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