A parallel implementation of symmetric band reduction using PLAPACK
Yuan-Jye Jason Wu, Christian H Bischof, P. Alpatov · University of North Texas Digital Library (University of North Texas) · 1996
Successive band reduction (SBR) is a two-phase approach for reducing a full symmetric matrix to tridiagonal (or narrow banded) form. In its simplest case, it consists of a full-to-band reduction followed by a band-to-tridiagonal reduction. Its richness in BLAS-3 operations makes it potentially more efficient on high-performance architectures than the traditional tridiagonalization method. However, a scalable, portable, general-purpose parallel implementation of SBR is still not available. In this article, we review some existing parallel tridiagonalization routines and describe the implementation of a full-to-band reduction routine using PLAPACK as a first step toward a parallel SBR toolbox. The PLAPACK-based routine turns out to be simple and efficient and, unlike the other existing packages, does not suffer restrictions on physical data layout or algorithmic block size.