Homework Answers
Fixed point iteration and the Aitken's ◇2 method.
Suppose we have a fixed point iteration
P0, p1=g(p0), p2=g(p1)....
Once we have p0, p1, and p2, we can compute
P0`= p0- ((p1-p0)^2/(p2- 2p1+p0))
At this point we restart the fixed point iteration with p0=p0`
P3=p0`, p4=g(p3), p5=g(p4)
And compute p3` =p3 - ((p4-p3)^2)/(p5-2p4+p3)
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3 Find the root s of the following functions using both Newton's ulethod and the anat inethod using tol epa. . You will vood to experiment with the parameters po, pl, ad maxits. . For each root, visualize the iteration history of both methods by plotting the albsolute errors, as a function . Label the two curves (Newton's method and secaut...
When using the secant method, if the points of the two previous
iterations were (-3, 1) and (3, 0), what would
be the x value to be used for the next iteration? Give your answer
to 2 decimal places.
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