ISSN:
1531-5878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract The structure inherent to the centrosymmetric matrices is exploited to obtain factorization results leading to significant computational savings in many engineering applications. Several interesting properties of the matrices are discussed with a view toward algorithm computational complexity. It is shown that the multiplicative complexity involved in the process of principal component (eigen-value/eigenvector) extraction, and in the evaluation of the determinant and inverse of such matrices, can be reduced by nearly 75% by employing the results presented here. The theory presented hereunifies andgeneralizes previous computationally efficient results onseveral specialized generalized centrosymmetric matrices; for example, the class of symmetric centrosymmetric (or doubly symmetric) matrices is shown to be a special case of the class of centrosymmetric matrices, and since the results obtained here are applicable over the field of complex numbers, the factorization results available for centrosymmetric matrices are readilyextended to the complex field. The centrosymmetric matrices play an important role in a number of areas such as pattern recognition, antenna theory, mechanical and electrical systems, and quantum physics. Specific examples of pattern recognition feature selection, a uniform linear antenna array, vibration in structures, and the quantummechanical oscillator are discussed to demonstrate that the theory developed here has a wide range of applications. In addition, certain specialized cases of the centrosymmetric matrices have, in the past, proved their indisputable usefulness in the areas of communication theory, digital filters, linear systems, linear prediction, and speech analysis.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01598746
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