Efficient Parallel Reduction of Bandwidth for Symmetric Matrices

Bandwidth reduction can be a first step in the computation of eigenvalues and eigenvectors for a wide-banded complex Hermitian (or real symmetric) matrix. We present algorithms for this reduction and the corresponding back-transformation of the eigenvectors. These algorithms rely on blocked Householder transformations, thus enabling level 3 BLAS performance, and they feature two levels of parallelism. The efficiency of our approach is demonstrated with numerical experiments.