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We develop an algorithmic framework for reducing the bandwidth of symmetric matrices via orthogonal similarity transformations. This framework includes the reduction of full matrices to banded or tridiagonal form and the reduction of banded matrices to narrower banded or tridiagonal form, possibly in multiple steps. Our framework leads to algorithms that(More)
We present a software toolbox for symmetric band reduction, together with a set of testing and timing drivers. The toolbox contains routines for the reduction of full symmetric matrices to banded form and the reduction of banded matrices to narrower banded or tridiagonal form, with optional accumulation of the orthogonal transformations, as well as(More)
Article history: Available online xxxx Keywords: Electronic structure calculations Eigenvalue and eigenvector computation Blocked Householder transformations Divide-and-conquer tridiagonal eigensolver Parallelization a b s t r a c t The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many(More)