Parallel preconditioned solvers are presented to compute a few extreme eigenvalues and -vectors of large sparse Hermitian matrices based on the Jacobi-Davidson (JD) method by G.L.C. Sleijpen and H.A. van der Vorst. For preconditioning, an adaptive approach is applied using the QMR (Quasi-Minimal Residual) iteration. Special QMR versions have been developed for the real symmetric and the complex Hermitian case. To parallelise the solvers, matrix and vector partitioning is investigated with a data distibution and a communication scheme exploiting the sparsity of the matrix. Synchronization overhead is reduced by grouping inner products and norm computations within the QMR and the JD iteration. The efficiency of these strategies is demonstrated on the massively parallel systems NEC Cenju-3 and Cray T3E.
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机译：提出了并行预处理求解器以计算基于G.L.C的Jacobi-Davidson（JD）方法来计算几个极端的特征值和大稀疏隐藏矩阵的Virce。 sleijpen和h.a. van der vorst。为了预处理，使用QMR（准剩余残差）迭代来应用自适应方法。已经为真正对称和复杂的隐士案件开发了特殊的QMR版本。为了使求解器，矩阵和向量分区进行研究，并利用数据脱模和利用矩阵的稀疏性的通信方案来研究。通过在QMR和JD迭代中分组内部产品和规范计算来减少同步开销。在大型平行系统NEC CENJU-3和CRAY T3E上证明了这些策略的效率。
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