Matrices that are characterized by off-diagonal decay, or more generally localization
of their entries, appear in applications throughout the mathematical and computational
sciences. The presence of such localization can lead to computational savings by designing faster numerical methods, since it
allows to (closely) approximate a given matrix by using its significant entries only, and
discarding the negligible ones according to a pre-established criterion. In this context
it is then of great practical interest to know a priori how many and which of these
entries can be discarded as insignicant. Many authors have therefore studied decay
rates for different matrix classes and functions of matrices.
An important example in this context is given by the (nonsymmetric) diagonally
dominant matrices, and in particular the diagonally dominant tridiagonal matrices. It is known that the entries of the inverse decay
with an exponential rate along a row or column, depending on whether the given matrix
is row or column diagonally dominant.
- Trainer/in: Reinhard Nabben