Equivalence to Gauss-Newton Method

If we compare Equations 6.79 and 6.11 we notice that the only difference between the quasilinearization method and the Gauss-Newton method is the nature of the equation that yields the parameter estimate vector k(l+l). If one substitutes Equation 6.81 into Equation 6.79 obtains the following equation 

By taking the last term on the right hand side of Equation 6.83 to the left hand side one obtains Equation 6.11 that is used for the Gauss-Newton method. Hence, when the output vector is linearly related to the state vector (Equation 6.2) then the simplified quasilinearization method is computationally identical to the Gauss-Newton method. 

Kalogerakis and Luus (1983b) compared the computational effort required by Gauss-Newton, simplified quasilinearization and standard quasilinearization methods. They found that all methods produced the same new estimates at each iteration as expected. Furthermore, the required computational time for the Gauss-Newton and the simplified quasilinearization was the same and about 90% of that required by the standard quasilinearization method. 

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