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