Selected Recent Applications of Sparse Grids

DOI10.4208/NMTMA.2015.W05SIzbMath1340.65213OpenAlexW2116111476MaRDI QIDQ3462936

Hans-Joachim Bungartz, Dirk Pflüger, Christoph Kowitz, Benjamin Peherstorfer

Publication date: 15 January 2016

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/nmtma.2015.w05si

zbMATH Keywords

interpolationsparse gridsnumerical quadratureBlack-Scholes modelcombination techniqueuncertainty quantificationhierarchical decompositionfinancial product pricingplasma turbulence simulations

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Numerical interpolation (65D05) Turbulence (76F99) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical quadrature and cubature formulas (65D32) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)

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A Multigrid Method for Adaptive Sparse Grids ⋮ Optimization of black-box problems using Smolyak grids and polynomial approximations ⋮ Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation ⋮ Sampling inequalities for sparse grids ⋮ From Data to Uncertainty: An Efficient Integrated Data-Driven Sparse Grid Approach to Propagate Uncertainty ⋮ Fast sparse grid operations using the unidirectional principle: a generalized and unified framework ⋮ Hierarchical extended B-splines for approximations on sparse grids

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