Research Of Matrix Parallel Algorithm Based On MPI

Matrix is a basic concept in the Numerical Algebra field. Many scientific computing problems come down to the matrix operations, such as numerical weather prediction, three-dimensional image processing and seismic analysis. Many matrix operations, such as large-scale matrix multiplication and the solution of eigenvalues of the matrix, require a large memory and a time-consuming process, so a single processor cannot stand anymore. Therefore, it is very important to effectively apply large-scale parallel matrix multiplication in practical applications.The object of parallel computing is to assign the tasks among different processors, namely task partitioning and processor mapping. In other words, we should allocate the tasks to multiple processors of a computer system rationally, make the work load of all processors to be relatively balanced, obtain better parallelism, and make the whole computer system complete processing tasks in a short period of time. In addition, the interaction among the processors should be decreased, in order to reduce the data exchange between processors and data communication costs.Taking the parallel algorithm and its application as the main topic of this thesis, we focus on the parallel algorithm of matrix multiplication and implementation of the algorithm on the IBM x3500 four-core server. Firstly, we outline the basic knowledge of parallel computing. Secondly, we introduce parallel algorithm determine factors of its performance. Finally, we introduce parallel algorithm programming environment. Mainly contributions are as follows:(1) Implementation of the parallelism of matrix operation. The matrix operations in the matrix-vector multiplication and matrix multiplication algorithm are described in detail and analyzed with implementation of the parallel algorithm in the MPI parallel environment. Comparing analysis of the result shows its necessity to apply matrix operations in large-scale for calculation.(2) Solution of the eigenvalues of matrix. In many practical problems, we only needs to calculate the largest eigenvalue of absolute value, but not request all the characteristics of the value matrix. We also give a realization of the largest eigenvalue for solving the parallel algorithm, implement the algorithm and analyze the results.(3)Application of matrix parallel algorithms in graph theory. Shortest path algorithm in graph theory is a classical problem. This thesis analyses the parallel algorithm for shortest path between two points, gives the parallel implementation of the methods. Theory analysis and experiment results show that the parallel algorithm has a higher parallel efficiency.