Parallel Tridiagonalization through Two-Step Band Reduction

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 tridiagonal-ization algorithm by Lang. In particular, we are able to express the update of the orthogonal transformation matrix in terms of block transformations. This expression leads to an algorithm that is almost entirely based on BLAS-3 kernels and has greatly improved data movement and communication characteristics. We also present some performance results on the Intel Touchstone DELTA and the IBM SP1.