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The application of parallel algorithm on the numerical calculation

机译：并行算法在数值计算中的应用

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In the rapid development of high-performance parallel computing technology today, the demand of science and engineering numerical calculation is higher and higher. In the numerical calculations, the final solution is converted into the calculation of large-scale system of linear equations. This article focuses on parallel algorithm of tridiagonal equations. Firstly, introduce the current solving tridiagonal linear equations on parallel algorithms: direct solution and the iterative solution. Direct solution, the algorithm is rich, the program is easy to implement, but the amount of calculation is too large, and most of the algorithms for the requirement of the coefficient matrix is relatively high. Iterative solution is more suitable for nonzero elements, especially the iteration solution combination with Krylov subspace. Then, by using the orthogonal projection method, greedy method and partition strategy method, a new parallel iterative procedure is used to solve arbitrary tridiagonal equations. Finally, give a new proof of convergence of the algorithm.
机译：在高性能并行计算技术飞速发展的今天，科学和工程数值计算的要求越来越高。在数值计算中，最终解被转换为大型线性方程组的计算。本文重点介绍三对角方程组的并行算法。首先，介绍当前在并行算法上求解三对角线性方程组的方法：直接解法和迭代解法。直接解决方案，算法丰富，程序易于实现，但计算量太大，且大多数算法对系数矩阵的要求较高。迭代解更适合于非零元素，尤其是与Krylov子空间结合的迭代解。然后，通过正交投影法，贪婪法和分区策略法，采用新的并行迭代程序求解任意三对角方程。最后，给出了该算法收敛性的新证明。

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