Page 90 - Numerical methods for chemical engineering
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76 2 Nonlinear algebraic systems
2 initia ess 1 2 1 n er iter atins 11
1
1
1
2
1
2 2
1
Figure 2.10 Trajectory of Newton’s method with the initial guess (1,1).
initia ess 2 1 n er iter atins 21
2 1 2
2
2
1
12
1
1
1
2 1 1
1
Figure 2.11 Trajectory of Newton’s method with the initial guess (2,−1).
certainly appears as if the choice of updates could be improved, by moderating the tendency
of the algorithm to make large, erratic steps. A reduced-step algorithm is proposed later
that avoids generating these erratic steps and makes Newton’s method more robust. These
plots are generated by Newton 2D test.m.
