Solving nonlinear algebraic systems in MATLAB

The full Newton step at satisfies the Unear system 

Therefore, it is also a global minimum of the quadratic cost function 

If we were to apply a minimization algorithm to we woidd find the fiill Newton step 

We note, however, that p becomes erratic when we are far from the solution. We therefore expect there to be some trust radius (that we modify at each iteration) such that we expect the quadratic model ml l(p) to be a vaUd measure of locating the solution only if II II2 Af l. We obtain the update vector by solving the constrained problem 

This technique is the basis of the MATLAB routine fsolve, whose use is demonstrated below. A further discussion of the trnst-region method, and the efficient dogleg method of implementing it, is provided in Chapter 5. 

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