T "'J r "'is not invertible and the normal equations cannot be solved ( at least uniquely ).
12.
Giuliani will do relatively well in the city, would be my guess, which would somewhat frustrate the normal equation,
13.
Then, the individual normal equation matrices were combined and the resultant matrix solved to obtain the positions and the parameters.
14.
T " X " is rank, the normal equations can be solved directly by using the Cholesky decomposition " R"
15.
For example, when fitting a Lorentzian the normal equations matrix is not positive definite when the half-width of the band is zero.
16.
In this form they correspond to the coefficients obtained by inverting the matrix of the normal equations of ordinary least squares ( OLS ).
17.
:: My belated two cents : The confusion arises because function notation looks like a normal equation, but is in fact a different thing entirely.
18.
The normal equations matrix is not positive definite at a maximum in the objective function, as the gradient is zero and no unique direction of descent exists.
19.
Although this equation is correct, and can work in many applications, it is not computationally efficient to invert the normal equations matrix ( the Gramian matrix ).
20.
This minimization problem has a unique solution, provided that the " n " columns of the matrix \ mathbf X are linearly independent, given by solving the normal equations
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