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One and Multidimensional Numerical Interpolation Methods

  • Peter Jochum
Conference paper
  • 162 Downloads

Abstract

Given the interpolation points (xi,fi) (“knots”) we search for coefficients ai satisfying the interpolation condition [6]:
$${\rm{I(}}{{\rm{a}}_{\rm{o}}}{\rm{, \ldots ,}}{{\rm{a}}_{\rm{n}}}\,{\rm{;}}\,{{\rm{x}}_{\rm{i}}}{\rm{)}}\,{\rm{ = }}\,{{\rm{f}}_{{\rm{i}}\,{\rm{,}}\,}}\,{\rm{i}}\,\,{\rm{ = }}\,\,{\rm{0, \ldots ,m}}\,\,{\rm{(m}}\,{\rm{ = }}\,{\rm{n),}}\,{\rm{where}}\,{{\rm{x}}_{\rm{i}}}\, \in \,{{\rm{R}}^{\rm{N}}}\,{\rm{and}}\,{{\rm{f}}_{\rm{i}}}\, \in \,{\rm{R}}\,{\rm{(R}}\,{\rm{ = }}\,{\rm{real}}\,{\rm{space)}}{\rm{.}}$$
(1)

Keywords

Interpolation Problem Interpolation Point Interpolation Space Interpolation Condition Data Perturbation 
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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References

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    Hämmerlin, G., Hoffmann, K.H., Improperly Posed Problems and Their Numerical Treatment. ISNM 63, Birkhäuser Basel 1983 Google Scholar
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    Jawny,J., Jochum,P., Eiermann,W.; J. Steroid Biochem. 1984 20, No. 2, 595CrossRefGoogle Scholar
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    Jochum, P., Schrott, E.L., Anal. Chimica Acta 1984, 157, 211CrossRefGoogle Scholar
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    Lawson, C.L., Hanson, J.H.; Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, New Jersey 1974Google Scholar
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    Sharaf, M.A., Kowalski, B.R., Anal. Chem. 1982, 54, 1291CrossRefGoogle Scholar
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    Stoer,J.; Einführung in die Numerische Mathematik I, 4th Edition. Springer Berlin 1983Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Peter Jochum
    • 1
  1. 1.Softron GmbHGräfelfingFederal Republic of Germany

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