The propagation of uncertainty with non-Lagrangian interpolation

Abstract

A 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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