Author(s) :
Matthias Bollhöfer
,
Volker Mehrmann
Preprint series :
SFB 393 `Numerische Simulation auf massiv parallelen Rechnern' in Chemnitz, SFB393/98-05, 1998
MSC 2000
- 65F05 Direct methods for linear systems and matrix inversion
-
65F10 Iterative methods for linear systems
-
65F50 Sparse matrices
-
65Y05 Parallel computation
Abstract :
In this paper we discuss the nested use of the Sherman-Morrison-Woodbury formula for the solution of large
sparse linear systems. The method itself can be seen as a compromise between a direct and an iterative solution method
for the linear system. Based on a low rank splitting the rank of the remaining system will be successively reduced by
performing low rank updates. Even if an iterative process will fail this will lead to a direct solution of the system. The main
difficulty is the optimal choice of the low rank updates. Several strategies will be discussed and illustrated by several
examples.
Keywords :
Nonsymmetric systems, parallel computations, (nested) divide & conquer, Sherman-Morrison-Woodburyformula, large sparse matrices, low rank modifications