The SBR Toolbox { Software

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 repacking routines for storage rearrangement. The functionality and the calling sequences of the routines are described, with a detailed discussion of the \control" parameters that allow adaptation of the codes to particular machine and matrix characteristics. We also brieey describe the testing and timing drivers included in the toolbox. 1. INTRODUCTION Reduction to tridiagonal form is a major step in eigenvalue computations for symmetric matrices. The LAPACK library Anderson et al. 1995] includes the blocked Householder tridiagonalization algorithm for full matrices Golub and Van Loan 1989; Dongarra et al. 1989] (routines SYTRD for the reduction and ORGTR for building the transformation matrix) and a variant of Schwarz's rotation-based algorithm Schwarz 1968; Kaufman 1984] for banded matrices (routine SBTRD).