Title: Look-Ahead in the Two-Sided Reduction to Compact Band Forms for Symmetric Eigenvalue Problems and the SVD,
Abstract: We address the reduction to compact band forms, via unitary similarity
transformations, for the solution of symmetric eigenvalue problems and the
computation of the singular value decomposition (SVD). Concretely, in the first
case we revisit the reduction to symmetric band form while, for the second
case, we propose a similar alternative, which transforms the original matrix to
(unsymmetric) band form, replacing the conventional reduction method that
produces a triangular--band output. In both cases, we describe algorithmic
variants of the standard Level-3 BLAS-based procedures, enhanced with
look-ahead, to overcome the performance bottleneck imposed by the panel
factorization. Furthermore, our solutions employ an algorithmic block size that
differs from the target bandwidth, illustrating the important performance
benefits of this decision. Finally, we show that our alternative compact band
form for the SVD is key to introduce an effective look-ahead strategy into the
corresponding reduction procedure.