5 papers
Inverse acyclic Z-matrices, matrices of tree structure and shifted generalized ultrametric matrices
Reinhard Nabben
Inverses of acyclic or treediagonal matrices are nicely characterized in the landmarked paper by Klein \cite{KLe82}. But also in \cite{Nab01} a characterization of these inverses i…
Hidden decay in the inverses of acyclic matrices
Reinhard Nabben
It is well-known that the absolute values of the entries of the inverse of a diagonally dominant tridiagonal matrix decay away from the diagonal. Moreover, lower and upper bounds f…
Norm-based convergence bounds for nonsymmetric algebraic V-cycle multigrid methods
Reinhard Nabben, Ludwig Rooch
Recently a new approach to analyze and create algebraic multigrid methods (AMG) for nonsymmetric and indefinite matrices was established. Convergence is measured in general norms i…
Optimal transfer operators for nonsymmetric two-grid methods
Reinhard Nabben, Ludwig Rooch
Algebraic Multigrid (AMG) methods have been proven to be effective solvers for large-scale linear algebraic systems with Hermitian positive definite (HPD) matrix . For…
Factorized sparse approximate inverse preconditioning for singular M-matrices
Katherina Bick, Reinhard Nabben
Here we consider the factorized sparse approximate inverse (FSAI) preconditioner. We apply the FSAI preconditioner to singular irreducible M-matrices. These matrices arise e.g. in…