Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

Large-scale problems have always been a challenge for numerical computations. An
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …

It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

We give a short introduction to methods for the data-sparse approximation of matrices
resulting from the discretisation of non-local operators occurring in boundary integral …

The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

We present and study a novel numerical algorithm to approximate the action of $ T^\beta:=
L^{-\beta} $ where $ L $ is a symmetric and positive definite unbounded operator on a …

This article deals with the existence of blockwise low-rank approximants—so-called ℋ-
matrices—to inverses of FEM matrices in the case of uniformly elliptic operators with L∞ …

In this paper we construct an approximation to the solution x of a linear system of equations
A x= b of tensor product structure as it typically arises for finite element and finite difference …

Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große,
eventuell auch voll besetzte Matrizen. Es wird eine neuartige Methode dargestellt, die es …