对称正定矩阵的并行LDLT分解算法实现

基于网络机群这一新的并行环境和消息传递界面MPI给出了两种不带平方根的Cholesky并行分解算法，算法采用行卷帘存储方案和提前发送策略，从而减少了负载的不平衡，增加了计算通信的重叠，减少了通信时间。理论分析和数值试验均表明，算法具有较高的并行加速比和效率。

Algorithms of parallel LDLT decomposition for SPD matrices and their implementation

This paper presents two parallel Cholesky decomposition algorithms without square root based on networked PC cluster, a kind of new parallel environment, and Message Passing Interface (MPI). With the scheme of row wrap storage and the strategy of send ahead, the algorithms reduce the load imbalance and communicational time and raise the lap of computation and com-munication. The theoretical analysis and numerical experiments show that the algorithms have high parallel speedup ratio and efficiency.