Skip to main content
SpringerLink
Log in

Empirical Interpolation Decomposition

  • Published:
Acta Applicandae Mathematicae Aims and scope Submit manuscript

Abstract

Many physical problems need a multidimensional description and involve high dimensional spaces. Standard discretization techniques often lead to an excessive computation time. To solve this problem, we develop in this paper an empirical interpolation decomposition (EID) for multivariate functions. This method provides an approximate representation of a given function in separate form. Error estimates of the developed EID are derived and some properties are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Nouy, A.: Higher-order principal component analysis for the approximation of tensors in tree-based low rank formats. ArXiv preprint (2017)

  2. Khoromskij, B.: Tensors-structured numerical methods in scientific computing: survey on recent advances. Chemom. Intell. Lab. Syst. 110(1), 1–19 (2012)

    Article  MathSciNet  Google Scholar 

  3. Barrault, M., Maday, Y., Nguyen, N.C., Patera, A.T.: An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. 339(9), 667–672 (2004)

    Article  MathSciNet  Google Scholar 

  4. Maday, Y., Nguyen, N.C., Patera, A.T., Pau, S.: A general multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8(1), 383–404 (2008)

    Article  MathSciNet  Google Scholar 

  5. Eftang, J.L., Grepl, M.A., Patera, A.T.: A posteriori error bounds for the empirical interpolation method. C. R. Math. 348, 575–579 (2010)

    Article  MathSciNet  Google Scholar 

  6. Maday, Y., Mula, O.: A generalized empirical interpolation method: application of reduced basis techniques to data assimilation. In: Analysis and Numerics of Partial Differential Equations, pp. 221–235. Springer, Berlin (2013)

    Chapter  Google Scholar 

  7. Chen, P., Quarteroni, A., Rozza, G.: Weighted empirical interpolation method: a priori convergence analysis and applications. ESAIM: M2AN 48, 943–953 (2014)

    Article  MathSciNet  Google Scholar 

  8. Casenave, F., Ern, A., Lelièvre, T.: Variants of the Empirical Interpolation Method: symmetric formulation, choice of norms and rectangular extension. ArXiv preprint, arXiv:1508.05330 [math.NA]

Download references

Acknowledgements

This work was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11 LABX-0056-LMH, LabEx LMH.

Author information

Authors and Affiliations

  1. CMLA, École Normale Supérieure Paris-Saclay and CNRS, Paris, France

    Asma Toumi

  2. LMAC, Sorbonne University, University of Technology of Compiégne, Compiégne, France

    Florian De Vuyst

Authors
  1. Asma Toumi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Florian De Vuyst
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Asma Toumi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Toumi, A., De Vuyst, F. Empirical Interpolation Decomposition. Acta Appl Math 164, 49–64 (2019). https://doi.org/10.1007/s10440-018-0223-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-018-0223-9

Keywords

Search

Navigation