ABSTRACT
Supposing that the input matrix of algorithm is M0, the serial matrix Gaussian elimination algorithm can be divided into five steps: (1) splitting of the matrix, (2) reduction of pivot rows (Trsm), (3) reduction of non-pivot rows (Axpy), (4) computation of new pivot rows, (5) reduction of matrix row. In these steps, the second step is the most time-consuming. The main work of the paper is to optimize the algorithm on MIC, and realize the parallel of the algorithm. For the completeness of the paper, the equivalent form of M0 after step (1) and (2) is as follows:
M ~ A B C D
~ Id A B C D0
, (1)
where A is sparse upper triangular matrix, C is sparse matrix, B and D are dense matrixes, Id is unit matrix. A consists of pivot rows and pivot columns. B consists of pivot rows and non-pivot columns. C consists of non-pivot rows and pivot columns. D consists of nonpivot rows and non-pivot columns.
