To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic factor. We describe three possible piecewise multilinear hierarchical interpolation schemes in detail and conduct a numerical comparison. Furthermore, we document the features of our sparse grid interpolation software package spinterp for MATLAB. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 38 articles , 1 standard article )

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  1. Castrillón-Candás, Julio E.; Kon, Mark: Analytic regularity and stochastic collocation of high-dimensional Newton iterates (2020)
  2. Morrow, Zachary; Stoyanov, Miroslav: A method for dimensionally adaptive sparse trigonometric interpolation of periodic functions (2020)
  3. Wang, Zhong; Li, Yan: Guaranteed cost spacecraft attitude stabilization under actuator misalignments using linear partial differential equations (2020)
  4. Aiton, Kevin W.; Driscoll, Tobin A.: An adaptive partition of unity method for multivariate Chebyshev polynomial approximations (2019)
  5. Dolgov, Sergey; Scheichl, Robert: A hybrid alternating least squares-TT-cross algorithm for parametric PDEs (2019)
  6. Elman, Howard C.; Su, Tengfei: Low-rank solution methods for stochastic eigenvalue problems (2019)
  7. Khan, Arbaz; Powell, Catherine E.; Silvester, David J.: Robust preconditioning for stochastic Galerkin formulations of parameter-dependent nearly incompressible elasticity equations (2019)
  8. Bhaduri, Anindya; He, Yanyan; Shields, Michael D.; Graham-Brady, Lori; Kirby, Robert M.: Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis (2018)
  9. Elman, Howard C.; Silvester, David J.: Collocation methods for exploring perturbations in linear stability analysis (2018)
  10. Karvonen, Toni; Särkkä, Simo: Fully symmetric kernel quadrature (2018)
  11. Sai, Aditya; Kong, Nan: Characterising model dynamics using sparse grid interpolation: parameter estimation of cholera (2018)
  12. Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi: Reduced basis methods for uncertainty quantification (2017)
  13. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: Exploring the locally low dimensional structure in solving random elliptic PDEs (2017)
  14. Nagy, Stanislav; Gijbels, Irène: Law of large numbers for discretely observed random functions (2017)
  15. Sun, Xianming; Vanmaele, Michèle: Uncertainty quantification of derivative instruments (2017)
  16. Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai: Precomputing strategy for Hamiltonian Monte Carlo method based on regularity in parameter space (2017)
  17. Berrone, S.; Canuto, C.; Pieraccini, S.; Scialò, S.: Uncertainty quantification in discrete fracture network models: stochastic fracture transmissivity (2015)
  18. Elman, Howard C.; Forstall, Virginia: Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations (2015)
  19. Nance, J.; Kelley, C. T.: A sparse interpolation algorithm for dynamical simulations in computational chemistry (2015)
  20. Schillings, C.; Schulz, V.: On the influence of robustness measures on shape optimization with stochastic uncertainties (2015)

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