In the recent decade, there has been a growing interest in the
numerical treatment of high-dimensional problems. It is well known
that classical numerical discretization schemes fail in more than
three or four dimensions due to the curse of dimensionality. The
technique of sparse grids helps overcome this problem to some
extent under suitable regularity assumptions. This discretization
approach is obtained from a multi-scale basis by a tensor product
construction and subsequent truncation of the resulting
multiresolution series expansion. This volume of LNCSE is a
collection of the papers from the proceedings of the workshop on
sparse grids and its applications held in Bonn in May 2011. The
selected articles present recent advances in the mathematical
understanding and analysis of sparse grid discretization. Aspects
arising from applications are given particular attention.
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