MATLAB - Curve Fitting 1/x Function

Question

I'd like to find a way to fit a curve to a specific functional form, namely:

y=constant/x

Is there a good way to do this? My data is just a set of (x,y) pairs.

Solution 1

Sure, try this.

You can rewrite this equation as: y = c0 + c1*z where c0 and c1 are the constants you want to solve for and z = 1/x.

If you have n points, you can write one equation for each pair:

y1 = c0 + c1*z1
y2 = c0 + c1*z2
...
yn = c0 + c1*zn

You've got an (n x 1) vector of known y values on the left hand side. There's an (n x 2) matrix where the first column is all ones and the second column is the known vector of x values that multiplies a (2 x 1) vector of unknown coefficients c0 and c1.

Premultiply both sides by the (2 x n) transpose of the matrix and you'll have two equations for two unknown coefficients that you can solve easily.

Read this for details.

Solution 2

Do you have the optimization toolbox? If so, use the lsqcurvefit function.

a=lsqcurvefit(@(a,x) a(1)./x,1,x,y);
hold on
plot(x,y,'o') %plot data
plot(x,a./x) %fit