We address the reduction to compact band forms, via unitary similaritytransformations, for the solution of symmetric eigenvalue problems and the compu-tation of the singular value decomposition (SVD). Concretely, in the first case, werevisit the reduction to symmetric band form, while, for the second case, we pro-pose 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 Level3 Basic Linear Algebra Subroutines (BLAS)-based procedures, enhanced with look-ahead, to overcome the performance bottleneck imposed by the panel factorization.

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