%0 Journal Article
%T Approximation of integral operators by Green quadrature and nested cross approximation
%A Steffen B£¿rm
%A Sven Christophersen
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s00211-015-0757-y
%X We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in combination with quadrature to obtain a first approximation of the kernel function and then applies nested cross approximation to obtain a more efficient representation. The resulting $\mathcal{H}^2$-matrix representation requires $\mathcal{O}(n k)$ units of storage for an $n\times n$ matrix, where $k$ depends on the prescribed accuracy.
%U http://arxiv.org/abs/1404.2234v3