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We address the reduction to compact band forms, via unitary similaritytransformations, for the solution of symmetric eigenvalue problems and thecomputation of the singular value decomposition (SVD). Concretely, in the firstcase we revisit the reduction to symmetric band form while, for the secondcase, we propose a similar alternative, which transforms the original matrix to(unsymmetric) band form, replacing the conventional reduction method thatproduces a triangular--band output. In both cases, we describe algorithmicvariants of the standard Level-3 BLAS-based procedures, enhanced withlook-ahead, to overcome the performance bottleneck imposed by the panelfactorization. Furthermore, our solutions employ an algorithmic block size thatdiffers from the target bandwidth, illustrating the important performancebenefits of this decision. Finally, we show that our alternative compact bandform for the SVD is key to introduce an effective look-ahead strategy into thecorresponding reduction procedure.

Look-Ahead in the Two-Sided Reduction to Compact Band Forms for Symmetric Eigenvalue Problems and the SVD