Data Fitting

Polynomials in MATLAB

Consider the following code to plot the polynomial y = 2x⁶ - 12x⁴ + 2x³ - 4x² + 15x + 50 for x values between -2.8 and 2.8

xx = -2.8 : 0.01 : 2.8;
yy = 2*xx.^6 - 12*xx.^4 + 2*xx.^3 - 4*xx.^2 +15*xx + 50;
plot(xx, yy)

MATLAB allows a more efficient representation / calculation:

Data Fitting

Given data points (x_k, y_k), find a smooth function f(x) (e.g., to be able to find values between data data points).

Interpolation: f(x_k) = y_k for all k

Approximation: sum of the squares of the errors ( error_k = f(x_k) - y_k) is minimized

Interpolation

Assume data points (x_k, y_k) have been put into variables xdata, ydata.

Using polyfit

Using spline

Plot to determine how reasonable the fit is:

Approximation

Fitting polynomials

Fitting non-polynomials

Example: fit xdata, ydata to the curve y = ae^bx

Idea: convert the curve to something that looks like a polynomial