whose pseudoinverse is
Multiplying y by A , we obtain the coefficient vector
which corresponds to the quadratic polynomial
F(x) = 1.200 - 0.757x 0.214x2
as the closest-fitting quadratic to the given data, in a least-squares sense.
As a practical matter, we solve the normal equation (28.33) by multiplying y by AT and then finding an LU decomposition of AT A. If A has full rank, the matrix AT A is guaranteed to be nonsingular, because it is symmetric and positive-definite.