THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY

Y. N. Balonin, M. B. Sergeev


Read the full article 

Abstract

The algorithm and software for search and study of orthogonal bases matrices – minimax matrices (M-matrix) are considered. The algorithm scheme is shown, comments on calculation blocks are given, and interface of the MMatrix software system developed with participation of the authors is explained. The results of the universal algorithm work are presented as Hadamard matrices, Belevitch  matrices (C-matrices, conference matrices) and matrices of even and odd orders complementary and closely related to those ones by their properties, in particular, the matrix of the 22-th order for which there is no C-matrix. Examples of portraits for alternative matrices of the 255-th and the 257-th orders are given corresponding to the sequences of Mersenne and Fermat numbers. A new way to get Hadamard matrices is explained, different from the previously known procedures based on iterative processes and calculations of Lagrange symbols, with theoretical and practical meaning.


Keywords: orthogonal matrices, M-matrices, Hadamard matrices, Mersenne matrices, Fermat matrices, numerical methods, calculation algorithm
Copyright 2001-2017 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.

Яндекс.Метрика