For the NewtonRaphson method the region of attraction (or

Chapter , Problem 6.27

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For the NewtonRaphson method the region of attraction (or basin of attraction) for a particular solution is the set of all initial guesses that converge to that solution. Usually initial guesses close to a particular solution will converge to that solution. However, for all but the simplest of multi-dimensional, nonlinear problems the region of attraction boundary is often fractal. This makes it impossible to quantify the region of attraction, and hence to guarantee convergence. 6.25 has two solutions when x2 is restricted to being between ?p and p. With the x2 initial guess fixed at 0 radians, numerically determine the values of the x1 initial guesses that converge to the 6.25 solution. Restrict your search to values of x1 between 0 and 1.

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