Foundations of Computational Mathematics

, Volume 13, Issue 5, pp 763–787 | Cite as

Approximation of Parametric Derivatives by the Empirical Interpolation Method

  • Jens L. Eftang
  • Martin A. Grepl
  • Anthony T. Patera
  • Einar M. Rønquist
Article

Abstract

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory.

Keywords

Function approximation A priori convergence Empirical interpolation method Parametric derivatives Sensitivity derivatives 

Mathematics Subject Classification (2010)

G5G99 65D05 41A05 41A25 

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Copyright information

© SFoCM 2012

Authors and Affiliations

  • Jens L. Eftang
    • 1
  • Martin A. Grepl
    • 2
  • Anthony T. Patera
    • 1
  • Einar M. Rønquist
    • 3
  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Numerical MathematicsRWTH Aachen UniversityAachenGermany
  3. 3.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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