CHE/COSC/MATH 4340-01 Numerical Analysis
Computer Laboratory Assignment 03
Due Date: Thursday, 02/05/09
Fixed Point Iteration
This problem concerns with finding zeros of f(x) = x2−3x+2 using fixed point iteration. We have
learned in class that using iteration xn+1=g(xn)with g(x) = x2+2
3would give us r1=1, while with
g(x) = √3x−2 would give us r2=2.
•Using the original f(x), find two more g(x). Then write a MATLAB function to compute the fixed
point iteration with this g(x)and give an observation about the convergence of fixed point iteration
with these g(x). For example, you might want to comment about to which exact zero it converges,
how flexible is the initial iterate.
•Let en=r−xnbe the error at iteration level n. For each g(x)that you have discovered (there are
four of them), plot the ratio en/en−1against index nwith n=1,2,3,···40. Thus you should report
four different plots. What do you observe? Relate your assessment with the error analysis that we
established in class.
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