High dimensional polynomial interpolation on sparse grids

  title={High dimensional polynomial interpolation on sparse grids},
  author={Volker Barthelmann and Erich Novak and Klaus Ritter},
  journal={Adv. Comput. Math.},
We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many different function spaces. We report on numerical experiments for d = 10 using up to 652 065 interpolation points. 
Highly Influential
This paper has highly influenced 38 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 356 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications citing this paper.
Showing 1-10 of 221 extracted citations

357 Citations

Citations per Year
Semantic Scholar estimates that this publication has 357 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 25 references

Integration over an hypercube

  • R. Cools
  • Unpublished Manuscript
  • 1998
Highly Influential
5 Excerpts

Testing multidimensional integration routines

  • A C.
  • Genz
  • 1984
Highly Influential
9 Excerpts

On asymptotics and estimates for the uniform norms of the Lagrange interpolation polynomials corresponding to the Chebyshev nodal points

  • V. K. Dzjadyk, V. V. Ivanov
  • Analysis Math
  • 1983
Highly Influential
5 Excerpts

1997b): A unified approach to error estimates for interpolation on full and sparse Gauß-Chebyshev grids

  • F. Sprengel
  • Rostocker Math. Kolloq
  • 1997
Highly Influential
5 Excerpts

Interpolation and wavelets on sparse Gauss-Chebyshev grids

  • F. Sprengel
  • W. Haussmann et al., eds.: Multivariate…
  • 1997
Highly Influential
5 Excerpts

A multiscale method for the evaluation of Wiener integrals

  • E. Novak, K. Ritter, A. Steinbauer
  • in: Approximation Theory IX,
  • 1998
1 Excerpt

Similar Papers

Loading similar papers…