NGS: Cache Efficient and Parallel Householder Bidiagonalization

EIA-0103642Gary W. Howell佛罗里达理工学院CISE NGS：高速缓存高效和并行双对角化高速缓存高效减少到双对角形式允许在计算矩形矩阵的奇异值分解（SVD）中显着加速。 奇异值分解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）的最标准和稳定的方法。 因此，它是不断使用的研究人员在全国和世界各地。这一建议将导致加速在标准LAPACK的实现，也在并行计算包SCALAPACK。 这项工作也将扩展到并行的情况下，包括在SCALPACK的视图。 在并行情况下，优化器不仅必须考虑本地计算机体系结构和存储器层次结构的细节，而且还必须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.