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Comparison of Some Reduced Representation Approximations

  • Mario Bebendorf
  • Yvon Maday
  • Benjamin Stamm
Part of the MS&A - Modeling, Simulation and Applications book series (MS&A, volume 9)

Abstract

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE’s. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category.

Keywords

Singular Value Decomposition Principal Orthogonal Direction Interpolation Point Interpolation Operator Lebesgue Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute for Numerical SimulationUniversity of BonnBonnGermany
  2. 2.UPMC Univ. Paris 06, UMR 7598 LJLLParisFrance
  3. 3.Institut Universitaire de France and Division of Applied MathematicsBrown UniversityProvidenceUSA
  4. 4.CNRS, UMR 7598 LJLLParisFrance

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