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 42 articles , 1 standard article )

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  1. Elman, Howard C.; Liang, Jiaxing; Sánchez-Vizuet, Tonatiuh: Surrogate approximation of the Grad-Shafranov free boundary problem via stochastic collocation on sparse grids (2022)
  2. Castrillón-Candás, Julio E.; Nobile, Fabio; Tempone, Raúl F.: A hybrid collocation-perturbation approach for PDEs with random domains (2021)
  3. Castrillón-Candás, Julio E.; Xu, Jie: A stochastic collocation approach for parabolic PDEs with random domain deformations (2021)
  4. Peng, Ruifei; He, Yiqian; Yang, Haitian: An efficient numerical method to solve inverse fuzzy-uncertain viscoelastic problems of identification (2021)
  5. Castrillón-Candás, Julio E.; Kon, Mark: Analytic regularity and stochastic collocation of high-dimensional Newton iterates (2020)
  6. Morrow, Zachary; Stoyanov, Miroslav: A method for dimensionally adaptive sparse trigonometric interpolation of periodic functions (2020)
  7. Wang, Zhong; Li, Yan: Guaranteed cost spacecraft attitude stabilization under actuator misalignments using linear partial differential equations (2020)
  8. Aiton, Kevin W.; Driscoll, Tobin A.: An adaptive partition of unity method for multivariate Chebyshev polynomial approximations (2019)
  9. Dolgov, Sergey; Scheichl, Robert: A hybrid alternating least squares-TT-cross algorithm for parametric PDEs (2019)
  10. Elman, Howard C.; Su, Tengfei: Low-rank solution methods for stochastic eigenvalue problems (2019)
  11. Khan, Arbaz; Powell, Catherine E.; Silvester, David J.: Robust preconditioning for stochastic Galerkin formulations of parameter-dependent nearly incompressible elasticity equations (2019)
  12. 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)
  13. Elman, Howard C.; Silvester, David J.: Collocation methods for exploring perturbations in linear stability analysis (2018)
  14. Karvonen, Toni; Särkkä, Simo: Fully symmetric kernel quadrature (2018)
  15. Sai, Aditya; Kong, Nan: Characterising model dynamics using sparse grid interpolation: parameter estimation of cholera (2018)
  16. Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi: Reduced basis methods for uncertainty quantification (2017)
  17. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: Exploring the locally low dimensional structure in solving random elliptic PDEs (2017)
  18. Nagy, Stanislav; Gijbels, Irène: Law of large numbers for discretely observed random functions (2017)
  19. Sun, Xianming; Vanmaele, Michèle: Uncertainty quantification of derivative instruments (2017)
  20. Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai: Precomputing strategy for Hamiltonian Monte Carlo method based on regularity in parameter space (2017)

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