User`s guide

Parametric Fitting
3-41
Example: Rational Fit
This example fits measured data using a rational model. The data describes the
coefficient of thermal expansion for copper as a function of temperature in
degrees Kelvin.
To get started, load the thermal expansion data from the file
hahn1.mat, which
is provided with the toolbox.
load hahn1
The workspace now contains two new variables, temp and thermex:
• temp is a vector of temperatures in degrees Kelvin.
•
thermex is a vector of thermal expansion coefficients for copper.
Import these two variables into the Curve Fitting Tool and name the data set
CuThermEx.
For this data set, you will find the rational equation that produces the best fit.
As described in “Library Models” on page 3-16, rational models are defined as
a ratio of polynomials
where n is the degree of the numerator polynomial and m is the degree of the
denominator polynomial. Note that the rational equations are not associated
with physical parameters of the data. Instead, they provide a simple and
flexible empirical model that you can use for interpolation and extrapolation.
y
p
1
x
n
p
2
x
n 1–
… p
n 1+
+++
x
m
q
1
x
m 1–
… q
m
+++
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