Abstract: Employing an intrinsic property of the ORTHOMIN（m） algorithm and eliminating data interdependence for inner product computation in the ORTHOMIN（m） algorithm，an improved parallel ORTHOMIN（m） algorithm called IORTHOMIN（m） algorithm is established in this paper.The convergence of IORTHOMIN（m） algorithm is as same as ORTHOMIN（m） algorithm，but the times of the synchronization overhead are reduced by a factor of two when computed using the IORTHOMIN（m） algorithm on distributed memory cluster systems based on MPI environment.The numerical result and theoretical analysis prove that the performance of the IORTHOMIN（m） algorithm is better than that of the ORTHOMIN（m） algorithm.

Key words: ORTHOMIN（m） algorithm, parallel computation, synchronization overhead, non-symmetric sparse linear systems

摘要： 通过利用ORTHOMIN（m）算法的固有性质，消除ORTHOMIN（m）算法的内积计算数据相关性，给出了一种改进的ORTHOMIN（m） （IORTHOMIN（m））算法。同ORTHOMIN（m）算法对比，IORTHOMIN（m）算法与ORTHOMIN（m）算法有相同的收敛性，在基于MPI的分布式存储并行机群上进行并行计算时，同步开销次数减少为ORTHOMIN（m）算法的一半。数值计算结果与理论分析表明改进的IORTHOMIN（m）算法的性能要优于ORTHOMIN（m）算法。

关键词: ORTHOMIN（m）算法, 并行计算, 同步开销, 非对称稀疏线性方程组