广义Hermitian特征问题标准化转换的有效并行块算法

Efficient Parallel Blocked Algorithms for Generalized Hermitian Eigenproblem

广义Hermitian特征问题并行求解器的性能依赖于所选择的并行算法和矩阵的分布策略等诸多方面.基于块存储和快算法策略,提出了一个新的标准化转化的并行算法,该并行算法将Cholesky分解结合到广义特征问题标准化转换中,降低了已有并行算法的通信开销,并增加了算法的并行性.新算法可显著改善已有并行算法的性能和可扩展性.另外给出了一个有效求解具有多个右端项的三角矩阵方程AX=B的并行块算法.通过自主开发的特征问题并行软件包PSEPS的测试结果表明,并行算法比传统的并行算法快大约1倍,并具有较好的可扩展性.

The performance of a generalized eigenproblem solver relies on many factors,which include selected parallel algorithms and matrix mapping strategy.A new parallelization is presented,which combines the Cholesky into the transformation from generalized to standard form.By reducing the communication cost and extending the parallelism,the new algorithm can obviously improve the performance and scalability of the original algorithm.Moreover,an efficient parallel algorithm is proposed to compute a triangular AX=B with multiple right hand sides.From the tests using the parallel software PSEPS,the speed of the parallel algorithm is about two times that of the classical parallel algorithms,and it has better performance and scalability than the classical parallel algorithms.