厄米矩阵的三级并行J-Jacobi算法
Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices
AI总结：
针对厄米矩阵特征值和特征向量计算，提出三种并行块Jacobi算法，通过分块实现负载均衡并利用缓存加速，保持相对精度。
摘要：
本文描述了用于计算厄米矩阵特征值和特征向量的单边双曲Jacobi型算法的几种高效并行实现。通过适当的分块算法，在所有可用处理器/核心之间获得了几乎理想的负载均衡。类似的分块技术可用于利用每个处理器的本地缓存内存，以进一步加速过程。由于现代计算机架构的多样性，这里描述的每种算法可能成为特定硬件和给定矩阵大小的选择方法。所有提出的分块算法计算的相对精度与原始非分块Jacobi算法相似。
英文摘要：
The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal load balancing between all available processors/cores is obtained. A similar blocking technique can be used to exploit local cache memory of each processor to further speed up the process. Due to diversity of modern computer architectures, each of the algorithms described here may be the method of choice for a particular hardware and a given matrix size. All proposed block algorithms compute the eigenvalues with relative accuracy similar to the original non-blocked Jacobi algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
