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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 via orthogonal transformations, together with a testing and timing program. The toolbox contains drivers and computational 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(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)
We present a two-step variant of the \successive band reduction" paradigm for the tridiagonalization of symmetric matrices. Here we reduce a full matrix rst to narrow-banded form and then to tridiagonal form. The rst step allows easy exploitation of block orthogonal transformations. In the second step, we employ a new blocked version of a banded matrix(More)
Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit(More)