Math-305, Numerical Methods & Matrices
Section 1.5 — Fixed Point Method

Dr. Kevin G. TeBeest

 

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 near the root? See the lecture for the answer.

  6. What will the Fixed Point Method do if g'(x) = -0.8 near the root? See the lecture for the answer.

  7. What will the Fixed Point Method do if g'(x) = 1.1 near the root? See the lecture for the answer.

  8. What is the rate of convergence of the fixed point method?
    Linear? Quadratic? Cubic? Exponential?

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