A partitioning scheme and iterative solution for sparse bordered systems (Q1098226)

Sparse bordered matrix systems arise in certain classes of problems. An example is the Jacobian system for the finite difference for finite element approximation and continuation solution of nonlinear PDE's. We develop a partitioning scheme that can be exploited in residual-based iterative methods and permits easy implementation in existing software. The scheme has been examined for several iterative methods, and particularly the Lanczos algorithms which proves very effective for the representative nonlinear test problems examined. The scheme vectorizes well and performance studies on vectorized supercomputers are given.