Consider the nonlinear equation f(x) = x3− 2x2 − x + 2 = 0. (a) Verify...

Consider the nonlinear equation f(x) = x³− 2x² − x + 2 = 0.

(a) Verify that x = 1 is a solution.

(b) Convert f(x) = 0 to a fixed point equation g(x) = x where this is not the fixed point iteration implied by Newton’s method, and verify that x = 1 is a fixed point of g(x) = x.

(c) Convert f(x) = 0 to the fixed point iteration implied by Newton’s method and again verify that x = 1 is a fixed point.

(d) Write MATLAB code to iterate on your fixed point iteration as well as the fixed point iteration implied by Newton. Compare these results based on x0 = 1.1. How fast did Newton converge? How fast did your iteration from part b converge (or did it at all)? What does the theory of fixed points tell you about these convergence results?

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Expert Solution

Colby Messinger answered 1 year ago

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