74 citations · 77 across the 8 of their papers we have counts for
10 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…
A two-level shifted Laplace preconditioner for Helmholtz problems: Field-of-values analysis and wavenumber-independent convergence
Luis García Ramos, Reinhard Nabben
One of the main tools for solving linear systems arising from the discretization of the Helmholtz equation is the shifted Laplace preconditioner, which results from the discretizat…