This paper presents an overview of the singular boundary method (SBM) and its various
engineering applications. The basic concepts of the singular boundary method are first …

The computational solution of problems can be restricted by the availability of solution
methods for linear (ized) systems of equations. In conjunction with iterative methods …

This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

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

A number of problems in probability and statistics can be addressed using the multivariate
normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a …

A class of matrices (\CalH-matrices) is introduced which have the following properties.(i)
They are sparse in the sense that only few data are needed for their representation.(ii) The …

Linear-scaling methods, or methods, have computational and memory requirements which
scale linearly with the number of atoms in the system, N, in contrast to standard approaches …

The first book dedicated to this new and powerful computational method begins with a
comprehensive description of MCTDH and its theoretical background. There then follows a …

This article considers the problem of approximating a general asymptotically smooth
function in two variables, typically arising in integral formulations of boundary value …

This book presents a unified theory of the Finite Element Method and the Boundary Element
Method for a numerical solution of second order elliptic boundary value problems. This …