NGS: Cache Efficient and Parallel Householder Bidiagonalization

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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.