Final answer:
To determine the coefficients of a quadratic polynomial that best fits a given set of data points using the least squares method in MATLAB, you can write a user-defined function named QuadFit.
Step-by-step explanation:
To determine the coefficients of a quadratic polynomial that best fits a given set of data points using the least squares method, you can write a MATLAB user-defined function as follows:
function a = QuadFit(x, y)
A = [x'.^2, x', ones(length(x), 1)];
a = (A' * A) \ (A' * y');
end
In this function, x and y are the input vectors with the coordinates of the data points, and a is the output vector with the values of the coefficients a0, a1, and a2.
To use this function with the given data points, you can call it as follows:
x = [4, -1, -7, 20, 0, 3, -15, 5];
y = [2, -2, 5, 5, -10, 7, 14, 5];
a = QuadFit(x, y);
The resulting coefficients are a0 = a(3), a1 = a(2), and a2 = a(1).
The MATLAB function 'QuadFit' calculates the coefficients of a quadratic polynomial using the least squares method, which minimizes the sum of squared errors of the predicted polynomial values from the given data points.
The task is to write a MATLAB function called QuadFit that calculates the coefficients of a quadratic polynomial f(x) = ax2 + bx + c using the least squares method. This method minimizes the sum of the squares of the differences between the observed and predicted values. The function takes two vectors x and y containing the data points and returns a vector a with the coefficients a2, a1, and a0 of the polynomial.
To use the function to find the quadratic polynomial that best fits the given data points, you can follow this MATLAB code:
function a = QuadFit(x, y)
% Construct the Vandermonde matrix
X = [x.^2, x, ones(length(x), 1)];
% Calculate the coefficients
a = X\y;
end
Upon calling QuadFit with the provided x and y values, it will return the coefficients of the best fit quadratic polynomial.