A parallel balance scheme for banded linear systems
Gene Howard Golub, Ahmed Sameh, Vivek Sarin · Numerical Linear Algebra with Applications · 2001
Abstract A parallel algorithm is proposed for the solution of narrow banded non‐symmetric linear systems. The linear system is partitioned into blocks of rows with a small number of unknowns common to multiple blocks. Our technique yields a reduced system defined only on these common unknowns which can then be solved by a direct or iterative method. A projection based extension to this approach is also proposed for computing the reduced system implicitly, which gives rise to an inner–outer iteration method. In addition, the product of a vector with the reduced system matrix can be computed efficiently on a multiprocessor by concurrent projections onto subspaces of block rows. Scalable implementations of the algorithm can be devized for hierarchical parallel architectures by exploiting the two‐level parallelism inherent in the method. Our experiments indicate that the proposed algorithm is a robust and competitive alternative to existing methods, particularly for difficult problems with strong indefinite symmetric part. Copyright © 2001 John Wiley & Sons, Ltd.