Preface to BIT 54:2

Abstract

Now we are back with a set of contributions from the regular stream of incoming BIT manuscripts. We note that several contributions deal with algorithms for time propagation, where the system is linear and the linear algebra is crucial for the success of a numerical algorithm for propagation in time, see the papers by Arnold, Bodendiek and Freitag. The last paper by Yan, deals with propagation governed by a fractional derivative. The papers byNovati andSundealwith regularization of ill posed problems, while those of Goda, Kressner and Ling treat empirical approximation problems. We have the two papers by Juntunen and Lamichhane that handle finite elements, and the one by Barreras on high relative accuracy issues in numerical linear algebra. These are the papers: Andreas Arnold andTobias Jahnke study a systemof ordinary differential equations, where the unknown is amultidimensional tensor, represented in the hierarchical Tucker format. This way, the time propagation can be described in fewer dimensions than for general tensors. It opens up for handling some practically interestingmodels in physics chemistry and economics. Alvaro Barreras and Juan Manuel Pena describe a subtraction free algorithm for LDU decomposition of an almost diagonally dominant Z-matrix. It is marginally more expensive than Gaussian elimination and expands the class of linear systems that can be solved with high relative accuracy. Andre Bodendiek and Matthias Bollhofer describe an adaptive-order rational Arnoldi method for moment matchingmodel reduction of a descriptor system, coming from time dependent Maxwell equations in computational electromagnetism. Crucial