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# Fit, Interpolation, or Polynomial Interpolation in Uncertain Calculus

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.
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

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

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