You should always perform 3 or 4 iterations of my classroom example(s) BEFORE attempting the homework.

1. Do these problems (click).

2. Review how to plot multiple functions on a common plot in the Maple Tutorial entitled Basics if necessary.

3. Under what conditions is the fixed point method guaranteed to converge? Answer in a complete and comprehensible sentence.

4. Under what conditions will the fixed point method converge faster? Answer in a complete and comprehensible sentence.

5. What will the fixed point method do if g'(x) = 0.2 in a neighorhood of the root? Specifically, will the fixed pt mthd converge to the root? If so, will the convergence be fast or slow?

6. What will the fixed point method do if g'(x) =  – 0.8 in a neighborhood of the root? Specifically, will the fixed pt mthd converge to the root? If so, will the convergence be fast or slow?

7. What will the fixed point method do if g'(x) = 1.1 in a neighborhood of the root? Specifically, will the fixed pt mthd converge to the root? If so, will the convergence be fast or slow?

8. What will the fixed point method do if g'(x) =  – 1 at the root itself?
   
   1. The fixed pt mthd will converge to the root.
   2. The fixed pt mthd will diverge from the root.
   3. It is not known whether the fixed pt mthd will converge or diverge.

9. What is the rate of convergence of the fixed point method?
   Linear? Quadratic? Cubic? Quartic? Quintic? Exponential?

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