Fit, Interpolation, or Polynomial Interpolation in Uncertain Calculus

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Initially there is one locator, representing a point in a region defined by the popup menu "axes scale". Each point is labeled , where is the current number of the locator, is its vertical coordinate, and is the uncertainty of as set by the slider. The popup menu "point" connects a point to the "uncertainty" slider. Deleting locators reorders the numbers and the "point" number jumps to zero, which means the slider is not connected to any point.

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The controls let you: • select one of the Mathematica built-in functions Fit, Interpolation, or InterpolatingPolynomial • change the axes scale to vary the range of the plot in steps from to • select the color of the interpolation curve • select the order of interpolation; changing the function to InterpolatingPolynomial automatically adjusts this parameter • connect the "point" popup menu with the uncertainty slider

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Contributed by: Valter Yoshihiko Aibe and Mikhail Dimitrov Mikhailov, INMETRO, Brazil (July 2009)
Open content licensed under CC BY-NC-SA


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Details

The rules given in the initialization section are borrowed from the Uncertain Calculus, introduced in [1].

The Demonstration combines Demonstrations [2] to [5], interpolating and extending them to work with uncertain numbers for , explored also in [6] and [7]. In general, both and in a measured function are uncertain numbers and , but here it is assumed that . This assumption is based on the possibility to transfer the uncertainty to the enlarged uncertain of the uncertain number , where [8, p. 125]. Here is an estimated value of the derivative that could be obtained by successive approximations.

References:

[1] V. Y. Aibe and M. D. Mikhailov, "Uncertainty Calculus in Metrology," Proceedings of ENCIT 2008, 12th Brazilian Congress of Thermal Engineering and Sciences, Belo Horizonte, MG, Brazil, November 10–14, 2008.

[2] Interpolating Polynomial

[3] Interpolating a Set of Data

[4] Fitting a Curve to Five Points

[5] Curve Fitting

[6] Solving Matrix Systems with Real, Interval, or Uncertain Elements

[7] Area, Perimeter, and Diagonal of a Rectangle with Uncertain Sides

[8] José Henrique Vuolo, Fundamentos da Teoria de Erros, 2nd ed., 2nd printing, Sao Paulo, Brazil: Edgar Blucher, LTDA, 2000.



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