提出了一种并行求解非对称块三对角线性方程组的方法.该方法通过对传统的预处理共轭梯度法的预条件子进行重新构造,使之适合并行计算.该算法只需相邻两台机子间通信,降低了通信次数易于求解.并从理论上分析文中算法的收敛性,给出了该算法的收敛性优于Gauss-seidel的预处理共轭梯度法的充分条件.最后,在HP rx2600集群上,进行了数值试验,结果表明实算与理论是一致的,并行性好,且迭代次数也明显降低.%Sections 1,2 and 3 of the full paper explain our algorithm, which we believe is more efficient than that of Ref. 3; we also believe that it is better in that the mathematics is more complete and rigorous. Section 1 starts from Ref. 3 and gives a better construction of the preconditioner of the traditional precondition conjugate gradient method. The better construction is suitable for parallel computing; our algorithm only needs the communication between two adjacent processors, thus reducing the amounts of time of communication. Section 3 analyzes the convergence of our algorithm in theory and obtains a sufficient condition for the algorithm; the convergence is superior to the preconditioners of the block Jacobi precondition matrix and the preceprocessing method of the block Gauss-Seidel precondition matrix; what are particularly worth paying attention to are Theorems 3. 2 and 3.4. Section 4 carries out the numerical simulation of our algorithm on the HP rx2600 cluster,the simulation results, given in Tables 1 and 2, and their analysis demonstrate preliminarily that our algorithm can do efficient parallel computing and solve large nonsymmetrical block-tridiagonal linear equations.
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