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 17 articles , 1 standard article )

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  1. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: Exploring the locally low dimensional structure in solving random elliptic PDEs (2017)
  2. Elman, Howard C.; Forstall, Virginia: Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations (2015)
  3. Nance, J.; Kelley, C.T.: A sparse interpolation algorithm for dynamical simulations in computational chemistry (2015)
  4. Torres Valderrama, Aldemar; Witteveen, Jeroen; Navarro, Maria; Blom, Joke: Uncertainty propagation in nerve impulses through the action potential mechanism (2015)
  5. Dinh, Vu; Rundell, Ann E.; Buzzard, Gregery T.: Experimental design for dynamics identification of cellular processes (2014)
  6. Griebel, Michael; Hamaekers, Jan: Fast discrete Fourier transform on generalized sparse grids (2014)
  7. Conrad, Patrick R.; Marzouk, Youssef M.: Adaptive Smolyak pseudospectral approximations (2013)
  8. Bazil, Jason N.; Buzzard, Gregory T.; Rundell, Ann E.: A global parallel model based design of experiments method to minimize model output uncertainty (2012)
  9. Borzì, A.; von Winckel, G.: A POD framework to determine robust controls in PDE optimization (2011)
  10. Borzì, A.: Multigrid and sparse-grid schemes for elliptic control problems with random coefficients (2010)
  11. Sankaran, Sethuraman; Audet, Charles; Marsden, Alison L.: A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation (2010)
  12. Agarwal, Nitin; Aluru, N.R.: A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties (2009)
  13. Borzì, A.; von Winckel, G.: Multigrid methods and sparse-grid collocation techniques for parabolic optimal control problems with random coefficients (2009)
  14. Ma, Xiang; Zabaras, Nicholas: An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)
  15. Ganapathysubramanian, Baskar; Zabaras, Nicholas: Sparse grid collocation schemes for stochastic natural convection problems (2007)
  16. Ganapathysubramanian, Baskar; Zabaras, Nicholas: Modeling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multiscale method (2007)
  17. Klimke, Andreas; Wohlmuth, Barbara: Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB. (2005)