MATLAB: Least square polynomial fit

least squaresmaximum

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?

Best Answer

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.
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