Campus Livre
polyfit
Least-squares polynomial fit to data.
Category: Mathematics > Elementary Math
Syntax
p = polyfit(x, y, n)Returns the coefficients of the degree-n polynomial that best fits y as a function of x in the least-squares sense.
Description
The function builds the Vandermonde matrix of x and solves the over-determined system by QR factorization. With n+1 points the polynomial passes exactly through the data (interpolation); with more points it minimizes the sum of squared residuals.
High degrees are numerically fragile because powers of x become nearly dependent. Keep the degree low, or center and scale x before fitting.
Input arguments
x, y- Vectors of the same length: sample points and measured values.
n- Degree of the polynomial. It needs at least
n+1distinct points for a unique fit.
Output arguments
p- Row vector of
n+1coefficients, highest power first, ready forpolyval.
Example
Line and parabola
x = [1 2 3 4];
y = [2 4 6 8.5];
p = polyfit(x, y, 1)
polyval(p, 5)
polyfit([0 1 2], [1 3 7], 2)Output
p = 1×2
2.1500 -0.2500
ans = 10.5000
ans = 1×3
1.0000 1.0000 1.0000