Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598555 | Linear Algebra and its Applications | 2016 | 16 Pages |
Abstract
Here we consider the iterative solution of linear systems of equations with a symmetric positive semidefinite system matrix. If multilevel methods in combination with Krylov subspace methods are used to find the solution of these systems, often singular subsystems or coarse grid systems have to be solved. Then the Moore-Penrose inverse of the coarse grid systems can be used. Here, we establish some theoretical techniques how to avoid the singularity of the coarse grid system, while the resulting operator remains the same as we would have used the Moore-Penrose inverse. One option is to delete specific columns of the restriction and prolongation operator. The other option is to perturb the system matrix.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
René Kehl, Reinhard Nabben,