Preliminary list of abstracts

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Sparse grid quadrature as a knapsack problem
Thu, 14:25--14:50
  • Leopardi, Paul (Mathematical Sciences Institute, Australian National University, Australia)
  • Hegland, Markus (Australian National University)

As pointed out by (e.g.) Griebel and Knapek [1], some sparse grid problems can be formulated and solved as continuous knapsack problems. The resulting solution is optimal in terms of estimated profit. In the case of sparse grid quadrature on weighted tensor products of reproducing kernel Hilbert spaces, the profit for each item is just the squared norm of a product difference rule, and this can be calculated precisely. This talk describes a particular sparse grid quadrature algorithm and shows that it is optimal in this more precise sense.

[1] M. Griebel, and S. Knapek, Optimized general sparse grid approximation spaces for operator equations, Mathematics of Computation, vol. 78, no. 268, pp. 2223-2257, 2009.