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Applying blocking technology to the computation of big dense matrices can make a better use of computerpsilas memory hierarchies and increase computing efficiency. The blocked algorithm for LU factorization is studied in this paper. Efficient algorithms are designed for the computation of the different matrix operations involved in the blocked LU factorization algorithm. Optimization techniques including matrix transposing and loop unrolling are used in the implementation of the matrix computations. Experimental results show that the block LU factorization algorithm runs much faster than the standard LU factorization. A speedup of more than 50% is achieved.