High dimensional polynomial interpolation on sparse grids

By Volker Barthelmann, Erich Novak, K. Ritter. Advances in Computational Mathematics, 2000

703 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f8d332548ef65a73e63bc04ece86b8504c32074c

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In Atomic and Molecular Physics, and Optics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Nonlinear Adventures at the Zero Lower Bound (2012, background): “See Barthelmann, Novak, and Ritter (2000) for details.”
Spline interpolation on sparse grids (2011, background): “A few basics and some references can be found in [2,42,43].”
Hyperbolic Cross Approximation (2016, methodology): “The reader can find some further results on numerical integration by Smolyak type methods in papers [328, 325] and [20, 252, 145, 253, 179].”
Non-intrusive reduced order modeling of nonlinear problems using neural networks (2018, background): “However, since reduced bases generally belong to nonlinear, matrix manifolds, standard interpolation techniques may fail, as they cannot enforce the constraints characterizing those manifolds, unless employing a large amount of samples [1, 4].”
Variance-based global sensitivity analysis for multiple scenarios and models with implementation using sparse grid collocation (2015, methodology): “The SGC techniques were developed for computing multidimensional integration (Smolyak, 1963), and have been shown to be an efficient and effective tool to overcome the curse of dimensionality for high dimensional numerical integration and interpolation (Barthelmann et al., 1999; Bungartz and Griebel”
Polynomial chaos expansions for dependent random variables (2019, methodology): “Stochastic collocation methods include pseudospectral projection [12, 14], sparse grid interpolation [4, 8], least orthogonal interpolation [43], least squares [40, 59], compressive sensing [17, 65, 29] and low-rank tensor decompositions [10, 18, 26].”
Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, methodology): “Dimension-adaptive sparse quadrature A host of useful methods are available for numerical integration [61, 62, 63, 64, 65, 66].”
Efficient Collocational Approach for Parametric Uncertainty Analysis (2007, background): “For details on construction and properties of sparse grid, see [3,18,19] and the reference therein.”
An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009, methodology): “To increase the convergence rate of this method, we are currently implementing the use of higher-order polynomials of local support as introduced in [24,28].”