Section: Optimization and Curve Fitting
polyfit
routine has the following syntax
p = polyfit(x,y,n)
where x
and y
are vectors of the same size, and
n
is the degree of the approximating polynomial.
The resulting vector p
forms the coefficients of
the optimal polynomial (in descending degree) that fit
y
with x
.
polyfit
routine finds the approximating polynomial
such that
is minimized. It does so by forming the Vandermonde matrix
and solving the resulting set of equations using the backslash
operator. Note that the Vandermonde matrix can become poorly
conditioned with large n
quite rapidly.
--> x = linspace(0,1,20); --> y = sin(2*pi*x); --> plot(x,y,'r-') --> quit
The resulting plot is shown here
Next, we fit a third degree polynomial to the sine, and use
polyval
to plot it
--> p = polyfit(x,y,3) p = 21.9170 -32.8756 11.1897 -0.1156 --> f = polyval(p,x); --> plot(x,y,'r-',x,f,'ko'); --> quit
The resulting plot is shown here
Increasing the order improves the fit, as
--> p = polyfit(x,y,11) p = 1.0e+02 * Columns 1 to 8 0.1246 -0.6855 1.3006 -0.7109 -0.3828 -0.1412 0.8510 -0.0056 Columns 9 to 12 -0.4129 -0.0000 0.0628 -0.0000 --> f = polyval(p,x); --> plot(x,y,'r-',x,f,'ko'); --> quit
The resulting plot is shown here