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The normal equation of motion of the particle is given as follows [21]:

First, the system is decoupled into a normal equation and an algebraic equation.

This latter equation is known as the normal equation of the least squares problem.

One can immediately think to invert the covariance matrix [C.sup.E.sub.k] in order to derive the Normal Equation matrix [N.sub.k].

The associated normal equation is ([R.sup.T] R + [S.sup.T] S)[??] + [R.sup.T]d = 0.

According to (10), the linear normal equation for [e.sup.mI] can be rewritten in the following form:

The normal equation method is based on the search of the minimum modulus of the residual error [epsilon] as expressed in the following equation,

Y = a+bx where a and b are constants whose values were obtained using normal equations. The result of the series analysis yield time series normal equation characteristic of Ekulu river stretch studied.

The equation (2.8) is a normal equation but (2.9) and (2.10) are not.

which is the normal equation, where [??](k) is the estimate of the filter tap weight vector in the least squares sense.

For example, the coordinates of the peak for beryllium are as follows: X = 60.9097, Y = 0.14796, the normal equation is Y = 0.0024292X.

By substituting the right-hand side of this last equation into the second normal equation, we also get two expressions for b (equation 11.7).

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