College of Science, Hebei Polytechnicy University, Tangshan 063009, China

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Abstract—This paper mainly designed a new method of using the Parallel LU Decomposition Algorithm for solving large-scale dense linear equations on the basis of the strategy of divide and rule，and analyzed the speedup and efficiency of the Parallel LU Decomposition Algorithm. In theory, it could improve the efficiency of problem-solving. In addition， the extension of Parallel LU Decomposition Algorithm，opened up a new idea of solving large-scale dense linear equations .This paper firstly introduced a solving method-LU decomposition algorithm of solving large-scale dense linear equations. And then described the related concepts and classification，the expression， the design and complexity metrics of the parallel algorithm etc. Put forwards the Parallel LU Decomposition Algorithm designed by the strategy of divide and rule． thus, conclusion that: In theory，it is not only more convenient and faster but reduces the computational complexity ， which the parallel LU decomposition algorithm for solving large dense matrix Finally，the parallel LU decomposition algorithm is used to solve a circling transportation problem.

Index Terms—LU Decomposition Algorithm, Parallel Algorithm, speedup and efficiency, inverse of matrix.

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Cite: Aimin Yang, Chunfeng Liu, Jincai Chang, Xiaoqiang Guo, "Research on Parallel LU Decomposition Method and It’s Application in Circle Transportation," Journal of Software vol. 5, no. 11, pp. 1250-1255, 2010.