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A note on the construction of L-fold sparse tensor product spaces
Journal
Constructive approximation
Volume
38
Number
2
Pages / Article-Number
235-251
Keywords
High-dimensional problems, Sparse grids, Sparse tensor product spaces, Tensor product domains of different dimensions, Sparse tensor product of ansatz spaces with different approximation power, Optimal construction of sparse grids, Rate of approximation
Abstract
In the present paper, we consider the construction of general sparse tensor product spaces in arbitrary space dimensions when the single subdomains are of different dimensionality and theassociated ansatz spaces possess different approximation properties. Our theory extends the results from Griebel and Harbrecht [Math. Comput., 82(282):975-994, 2013] for the construction of two-fold sparse tensor product space to arbitrary L-fold sparse tensor product spaces.
