改进的并行高斯全主元消去法

为减少Gauss全主元消法的运行时间，用多进程与多线程混合的方式对其进行了并行化，同时对该算法进行了改进．采用MPI并行I／O技术提高读取数据文件的速度，降低对内存的需求；采用标志数组避免了选主元后换行带来的通信开销；使用线程模型确定最优线程数，提高运行消去的速度；通过预先发布机制降低回代求解步骤的时间复杂度．实际运行结果表明，随着方程组阶数增大，加速比也逐渐增大，对于5000元的方程组，8进程同时运行，加速比可达6．68，并行效率稳定在0．85左右．这表明该算法具有可扩展性和稳定的并行效率，适用于大规模并行计算．

Improved Parallel Complete Gaussian Pivoting Elimination

To reduce the executing time of complete Gaussian pivoting elimination,it is parallelized in a man- ner combined multi-thread and multi-process,and improved at the same time.Message passing interface (MPI) parallel I/O technology is adopted to increase the speed of reading data files and reduce the requirement to memory.A flag array is used to avoid the communication cost caused by exchanging rows after finding pivot elements.A thread model is used to find the optimal number of threads,which speeds up the elimination.And the time complexity of backward substitution is reduced by preinforming strategy.Actual implementation shows that the speedup enhances as the number of equations increases,for a linear system of five thousand equations, the speedup of eight processes can be as high as 6.68,the parallel efficiency stabilizes at about 0.85.All these indicate that the algorithm has good scalability and stable parallel efficiency,and can be used in large-scaled parallel computation.