Abstract: PLASMA is a high performance linear algebra package. Its innovative approach such as block data layout with tiling,fine grain parallelism and out of order execution mechanism greatly improves the performance of the program. However, there arc still some problems, for example, the size of block plays a severe role in performance and this mechanism brings some data copy. In this paper, by comparing the traditional LAPACK and PLASMA's mechanism, we aimed to analyze the advantages and disadvantages of PLASMA, and proposed two methods to make up the disadvantages. As to the PLASMA architecture, we proposed a concept of marginal matrix and analysed their impact on performance via extensive testing and analysis, and then proposed a method of auto-tuning. Besides, we also found a way to further improve the performance of PLASMA，which is adopting data transmission and computing in parallel. Finally,we verified the effect of optimized method by doing a large number of testing.

Key words: LAPACK, PLASMA, Auto-tuning, Optimization