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Solving linear systems using decomposition.

Zaitsev, D.A.

In: Systems Investigations and Information Technologies, 2005, no. 2, pages 131-143. 2005. In Russian.

Abstract: Special subsets of equations of linear system named by clans were introduced and studied. It was proposed to use the decomposition into clans for the acceleration of solving of linear system. Complexity of decomposition equals cube depending on size of system. Therefore, acceleration of computations was obtained for methods with complexity exceeding cube. For solving of integer systems in nonnegative integer numbers acceleration of computations obtained is exponential.

Keywords: linear system; clan; decomposition; speed-up of computations.


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