Least square polynomial fit

I have two arrays x(i) ,y(i). I need to do a least square polynomial fitting for y(i). After the polynomial fit is done, I need to find the maximum of y(i), say y(n) and then corresponding to that find the value of x(n). Can you please suggest, how shall I proceed? What are the math functions involved?

Answer 1

[John D'Errico]

Learn to use matlab. By this, I mean learn how to look for the tools you need. So you want to find a polynomial model. A good idea is to learn the lookfor function.

lookfor polynomial

If you do this, you will find a tool for polynomial fitting - polyfit. It will also show you polyder, an important thing since you are looking for a maximum. A stationary point on a curve will come at a root of the derivative. Finally, you might notice roots.

So much to glean from a simple lookfor command.

I will add that the best programmatic solution is to use a better tool than a polynomial fit anyway. Polynomials are terribly poor tools for curve fitting. Instead, use a tool designed to do the job.

   x = rand(1,50);
   y = sin(pi*x) + randn(size(x))/100;
   slm = slmengine(x,y,'knots',8,'plot','on');

   [maxfun,maxloc] = slmpar(slm,'maxfun') 
   maxfun =
         0.99971
   maxloc =
         0.50241

Here, I used my slm tools (it is on the file exchange) to do the curve fitting. It includes a tool that will determine various parameters from the resulting model, one of which is the maximum value of the function, and the location thereof.

[Matt J]

Looks like the OP forgot to accept this one.

[B]

How would I use this process to find the polynomial equation if I know points on the curve?

Answer 2

[Dr. Seis]

Check out "polyfit", "polyval" and "max"

- polyfit will give you the polynomial coefficients for an n-order polynomial

- polyval will give you new y-values when you supply it new x-values and the polynomial coefficients found in polyfit

- max will give you the max value associated with you new y-values, it can also supply you the index of the max value so you can determine its corresponding value from your new x-values