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4 - Interpolation

Published online by Cambridge University Press:  04 August 2010

Andi Klein
Affiliation:
Los Alamos National Laboratory
Alexander Godunov
Affiliation:
Old Dominion University, Virginia
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Summary

An important part in a scientist's life is the interpretation of measured data or theoretical calculations. Usually when you do a measurement you will have a discrete set of points representing your experiment. For simplicity, we assume your experiment to be represented by pairs of values: an independent variable “x,” which you vary and a quantity “y,” which is the measured value at the point x. As an illustration, consider a radioactive source and a detector, which counts the number of decays. In order to determine the half-life of this source, you would count the number of decays N0, N1, N2, …, Nk at times t0, t1, t2, …, tk. In this case t would be your independent variable, which you hopefully would choose in such a way that it is suitable for your problem. However, what you measure is a discrete set of pairs of numbers (tk, Nk) in the range of (t0, tk). In order to extract information from such an experiment, we would like to be able to find an analytical function which would give us N for any arbitrary chosen point t. But, sometimes trying to find an analytical function is impossible, or even though the function might be known, it is too time consuming to calculate or we might be only interested in a small local region of the independent variable.

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Publisher: Cambridge University Press
Print publication year: 2006

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  • Interpolation
  • Andi Klein, Los Alamos National Laboratory, Alexander Godunov, Old Dominion University, Virginia
  • Book: Introductory Computational Physics
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511793219.005
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  • Interpolation
  • Andi Klein, Los Alamos National Laboratory, Alexander Godunov, Old Dominion University, Virginia
  • Book: Introductory Computational Physics
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511793219.005
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Interpolation
  • Andi Klein, Los Alamos National Laboratory, Alexander Godunov, Old Dominion University, Virginia
  • Book: Introductory Computational Physics
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511793219.005
Available formats
×