NGS: Cache Efficient and Parallel Householder Bidiagonalization

gary W. howell佛罗里达理工学院cise NGS：缓存效率和并行双对角化缓存效率降低到双对角形式可以显著加快矩形矩阵奇异值分解（SVD）的计算速度。SVD提供了解决最小二乘问题和提供低秩近似（允许压缩以矩阵形式存储的数据）的最标准和最稳定的方法。因此，它被全国和世界各地的研究人员不断使用。该提议将导致标准LAPACK实现和并行计算包SCALAPACK的速度加快。这项工作还将扩展到并行情况，以期包含在SCALPACK中。在并行情况下，优化器不仅要考虑本地计算机体系结构和内存层次结构的细节，还要考虑处理器之间的通信。

EIA-0103642Gary W. HowellFlorida Institute of TechnologyCISE NGS: Cache Efficient and Parallel BidiagonalizationCache efficient reduction to bidiagonal form allows a significant speedup in computation of the singular value decomposition (SVD) for rectangular matrices. The SVD provides the most standard and stable means of solving least square problems and of providing low rank approximations (allowing compressions of data stored in matrix form). As such it is used constantly by researchers around the nation and the world.This proposal will result in speedups in the standard LAPACK implementation and also in the parallel computation package SCALAPACK. The work will also extend to the parallel case with a view for inclusion in SCALPACK. In the parallel case the optimizer must take into account not only details of the local computer architecture and memory hierarchy but also communication among the processors.