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TitleThe propagation of uncertainty with non-Lagrangian interpolation
Publication TypeJournal Article
Year of Publication2001
AuthorsWhite, D.R.
Pagination63 - 69
Date Published2001
ISSN00261394 (ISSN)
KeywordsFourier transforms, Interpolation, Lagrange interpolation, Lagrange multipliers, Least squares approximations, MATHEMATICAL MODELS, Polynomial approximation, Trigonometric functions, Uncertain systems
AbstractA recent paper described the propagation of uncertainty with polynomial or Lagrange interpolation and demonstrated a number of mathematical results that simplify the calculation of uncertainty. This paper extends the analysis to any interpolation that can be expressed as a linear combination of functions. Examples of this form include Gauss, Fourier and linear least-squares interpolations, as well as a wide range of application-specific interpolations employing a combination of functional forms. Application of the results is illustrated by considering a number of the non-Lagrangian interpolation equations of the International Temperature Scale of 1990 (ITS-90). A comparison of Lagrange and least-squares approaches is used to highlight the benefits of the latter.

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