This is the second volume of a three-volume set comprising a comprehensive study of the
tractability of multivariate problems. The second volume deals with algorithms using …

Sparse grids allow one to employ grid-based discretization methods in data-driven
problems. We present an extension of the classical sparse grid approach that allows us to …

BIM-based tools can contribute to addressing some of the challenges faced by structural
engineering practitioners. A BIM-based framework for the development of components that …

In this article we introduce new methods for the analysis of high dimensional data in tensor
formats, where the underling data come from the stochastic elliptic boundary value problem …

While sparse grids allow one to tackle problems in higher dimensionalities than possible for
standard grid-based discretizations, real-world applications often come along with …

A multilevel kernel-based interpolation method, suitable for moderately high-dimensional
function interpolation problems, is proposed. The method, termed multilevel sparse kernel …

Moderately high-dimensional approximation problems can successfully be solved by
combining univariate approximation processes using an intelligent combination technique …

Substantial modifications of both the choice of the grids, the combination coefficients, the
parallel data structures and the algorithms used for the combination technique lead to …

Abstract Let X_n={x^ j\} _ j= 1^ n X n= xj j= 1 n be a set of n points in the d-cube I^ d:= 0, 1^ d
I d:= 0, 1 d, and Φ _n={φ _j\} _ j= 1^ n Φ n= φ jj= 1 na family of n functions on I^ d I d. We …

Gaining knowledge out of vast datasets is a main challenge in data-driven applications
nowadays. Sparse grids provide a numerical method for both classification and regression …