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82 2 Nonlinear algebraic systems
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Figure 2.13 Trajectory of reduced-step Newton method with the guess (2,2) (number of iterations =
6).
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Figure 2.14 Trajectory of reduced-step Newton method with the guess (1,1) (number of iterations =
6).
the function norm. The trust-region Newton method is more robust, especially when the
Jacobian is nearly singular, because it simultaneously varies both the step direction and
the step magnitude to find an acceptable reduction of the function norm. Being a form of
numerical optimization, a detailed discussion of this algorithm is postponed until Chapter
5; however, we present here the basic concepts.
