Direct Methods for Banded Linear Systems on Massively Parallel Processor Computers

The authors discuss direct methods for solving systems of linear equations Ax = b, A {element_of} lR{sup nxn}, on massively parallel processor (MPP) computers. Here, A is a real banded n x n matrix with lower and upper half-bandwidth r and s, respectively. We assume that the matrix A has a narrow band, meaning r + s << n. Only in this case, it is worthwhile taking into account the zero structure of A, i.e. store the matrix by diagonals and modify algorithms.