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Choix D'une Base Dans L'approximation D'une Fonction

  • J. Lemaire
  • M. Moriou
  • J. Pouget
Computational Techniques
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)

Abstract

Many models of physical, chemical and biological processes using the description of flow between cells lead to identifying the output of the type
. These particular problems are thoroughly studied in papers and various methods are proposed. After a detailed study of these various methods which consist in determining the parameters n, {ai}, {bi}, we have reached the following conclusions:

1o) that the adjustment of experimental results by multi exponential function may often be obtained with very good approximation.

2o) that the adjustment of these results is but slightly sensitive to the variation of the parameters n, {ai}, {bi}.

The interpretation of that last point is quite explicit in the case when the method used leads to solving a linear system. This one is always ill conditionned.

3o) that very few methods allow to approach an over estimation of the error on the various coefficients the approximation.

This last point is particularly dangerous in the case when the parameters ai and bi have physical significance particularly in medecine. We have defined for certain methods the function bases for which the conditionning was best, i.e. for which the errors on the coefficients ai were of the same magnitude order.

In the same way we have defined a spectral method using a moment method and allowing a calculus of the error of approximation.

Keywords

Exponential Decay Curve Steady State Multiplicity Random Difference Equation Asymptotic Regression Multi Exponential Function 
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.

Bibliographie

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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • J. Lemaire
    • 1
  • M. Moriou
    • 1
  • J. Pouget
    • 1
  1. 1.Département InformatiqueInstitut Universitaire de TechnologieNice CedexFrance

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