polyfit() in MATLAB

Polyfit is a function in MATLAB that fits a polynomial to a set of data points. It takes in three arguments:

x: a vector of x-coordinates of the data points
y: a vector of y-coordinates of the data points
n: the degree of the polynomial

polyfit returns a vector of coefficients representing the fitted polynomial in descending order. In this article, we will explore the polyfit function in MATLAB and how it can be used to fit a polynomial to a set of data points.

The syntax for polyfit is as follows:

Syntax:

p = polyfit(x,y,n)

where x and y are vectors of the same length representing the x- and y-coordinates of the data points, respectively, n is the degree of the polynomial, and p is a vector of coefficients representing the fitted polynomial in descending order.
 

Suppose we have the following data points:

(1,2) (2,3) (3,4)

We can use polyfit to fit a polynomial to these points. For example:

Example 1:

x = [1 2 3];
y = [2 3 4];
p = polyfit(x,y,1)

Output:

p = 1.0000  1.0000

Explanation:

This means that the fitted polynomial is of degree 1 (a straight line) and has the following form:

y = x + 1

We can use polyval, another built-in function in MATLAB, to evaluate this polynomial at a specific point x. For example:

Example 2:

x = 2;
y = polyval(p,x)

Output:

3.0000

This means that the value of the fitted polynomial at x = 2 is 3, which is the same as the original data point.

Multiple Degrees

We can also fit polynomials of a higher degree to the data points. For example, to fit a quadratic polynomial (degree 2). In MATLAB, the polyfit function can be used to fit a polynomial of any degree to a set of data points. The degree of the polynomial is specified as the third argument to the polyfit function.

Example 3:

x = [1 2 3];
y = [2 3 4];
p = polyfit(x,y,2)

Output:

p = -0.0000    1.0000    1.0000

Conclusion:

In conclusion, polyfit is a useful function in MATLAB for fitting a polynomial to a set of data points. It is simple to use and can save time when working with polynomials in your code.