matlab interpfit

interpfit is a function in MATLAB that generates a piecewise polynomial function that interpolates a set of data points. It uses the least-squares method to fit a polynomial to the data points, and then generates a piecewise polynomial function that passes through the data points.

The syntax for the interpfit function is:

p = interpfit(x,y)

where x and y are the vectors of data points, and p is the piecewise polynomial function that interpolates the data.

The interpfit function uses the following algorithm to generate the piecewise polynomial function:

1. Divide the data points into intervals, each of which will be interpolated by a polynomial of degree n.

2. For each interval, fit a polynomial of degree n to the data points using the least-squares method.

3. Connect the polynomials at the interval boundaries to create a continuous piecewise polynomial function.

The degree of the polynomial used to interpolate each interval (n) is determined by the number of data points in the interval. If there are fewer data points than the degree of the polynomial, then the function will not be able to interpolate the interval exactly. In this case, the function will use the least-squares method to find the best-fit polynomial that approximates the data points.