Propagation of Uncertainty and Comparison of Interpolation Schemes

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• 作者：D. R. White
• 关键词：Interpolation ; Lagrange interpolation ; Least ; squares ; Linear interpolation ; Measurement uncertainty ; Spline
• 刊名：International Journal of Thermophysics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：38
• 期：3
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Condensed Matter Physics; Classical Mechanics; Industrial Chemistry/Chemical Engineering; Physical Chemistry;
• 出版者：Springer US
• ISSN：1572-9567
• 卷排序：38

文摘

The numerical information in the calibration reports for indicating instruments is typically sparse, often comprising a simple table of corrections or indicated values against a small number of reference values. Users are left to interpolate between the tabulated values using one of several well-known interpolation algorithms, including straight-line, spline, Lagrange, and least-squares interpolation. Although these algorithms are well known, there has apparently been no comparison of their performance in respect of uncertainty propagation. This paper provides an overview of the advantages and disadvantages of the most common interpolation algorithms with respect to uncertainty propagation, immunity to interpolation error, and sensitivity to data spacing. Secondly, the paper illustrates an unconventional method for the uncertainty analysis. The method exploits the linear dependence of the interpolations on measurements of the interpolated quantity, and is easily applied to any linear functional interpolation. In many respects, the best all-round interpolation scheme is a polynomial fitted by least-squares methods, which has a low propagated uncertainty, continuity to the chosen order of the fitted polynomial, and a good immunity to large gaps in the data.