Parallel Algorithms for Banded Linear Systems
Stephen J. Wright · SIAM Journal on Scientific and Statistical Computing · 1991
A partitioned Gaussian elimination algorithm with partial pivoting which is suitable for multiprocessors with small to moderate numbers of processing elements is described. It is only assumed that the system is nonsingular; hence the submatrices in the chosen partitioning may be rank-deficient and this makes the algorithm more complex than those which have been proposed for diagonally dominant and symmetric positive-definite systems. Operation counts and stability are examined. Some numerical results obtained on Alliant FX/8 and Sequent Balance multiprocessors are presented.