Parallel Tridiagonalization through Two-Step Band Reduction (1994)
| Venue: | In Proceedings of the Scalable High-Performance Computing Conference |
| Citations: | 22 - 12 self |
BibTeX
@INPROCEEDINGS{Bischof94paralleltridiagonalization,
author = {Christian Bischof and Bruno Lang and Xiaobai Sun},
title = {Parallel Tridiagonalization through Two-Step Band Reduction},
booktitle = {In Proceedings of the Scalable High-Performance Computing Conference},
year = {1994},
pages = {23--27},
publisher = {IEEE Computer Society Press}
}
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Abstract
We present a two-step variant of the "successive band reduction" paradigm for the tridiagonalization of symmetric matrices. Here we reduce a full matrix first to narrow-banded form and then to tridiagonal form. The first step allows easy exploitation of block orthogonal transformations. In the second step, we employ a new blocked version of a banded matrix tridiagonalization 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. 1 Introduction Reduction to tridiagonal form is a major step in eigenvalue computations for symmetric matrices. If the matrix is full, the conventional Householder tridiagonalization approach [9, p. 276] or a block variant thereof...
