Abstract
In this paper we extend the study of (dimension) adaptive sparse grids by building a lattice framework around projections onto hierarchical surpluses. Using this we derive formulas for the explicit calculation of combination coefficients, in particular providing a simple formula for the coefficient update used in the adaptive sparse grids algorithm. Further, we are able to extend error estimates for classical sparse grids to adaptive sparse grids. Multi-variate extrapolation has been well studied in the context of sparse grids. This too can be studied within the adaptive sparse grids framework and doing so leads to an adaptive extrapolation algorithm.
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Harding, B. (2016). Adaptive Sparse Grids and Extrapolation Techniques. In: Garcke, J., Pflüger, D. (eds) Sparse Grids and Applications - Stuttgart 2014. Lecture Notes in Computational Science and Engineering, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-319-28262-6_4
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DOI: https://doi.org/10.1007/978-3-319-28262-6_4
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