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solving linear systems via composition of their clans解决线性系统通过组成自己的家族
Intelligent Info rmation Management, 2009, 1, 73-80 doi:10.4236/iim.2009.12012 Published Online November 2009 (http :///journal/iim) Solving Linear Systems via Composition of their Clans Dmitry A. ZAITSEV Odessa National Telecommunication Academy, Kuznechnay a, Odessa, Ukraine Email: zaitsev_dmitry@ mail.ru Abstract: The decomposition technique for linear system solution is proposed. This technique may be com- bined with any known method of linear system solution . An essential acceleration of computations is ob- tained. Methods of linear system solution depend on the set of numbers used. For integer and especially for natural numbers all the known methods are hard enough. In this case the decomposition technique described allows the exponential acceleration of computations. Keywords: linear system, decomposition, clans, acceleration of computation 1. Introduction solution in nonnegative integer numbers are exponential [2,4,9,12]. It makes significant difficulties in the applica- The task of linear system solution is a classical task of tion of these methods to real-life systems analysis. linear algebra [10]. There are a variety of known meth- For example, if the complexity of method is about 2q , ods for linear system solution. It should be noted that the where q is the dimension of the system, then to solve choice of the method depends essentially on the set of 30 numbers used. More precise it depends on the algebraic the system with dimension 100 it is req
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