Consider the equation in R, f(x)=0 with root and a method with the order of convergence p and the asymptotic error C_p. If N_p operations are performed and the initialization operation is ignored the total number of operations required to approximate the solution with precision is, where the basis of the logarithm is arbitrary, e₀ is the initial error.

b) Consider the algorithm whose step consists of two steps of Newton's method. What is the convergence order of the algorithm?

c) Using the idea from the previous point, show how arbitrary methods can be created to solve the equation f (x) = 0. Why is the order of a method not the sure selection criterion when solving a problem?

Indication: Consider e_n= |x_n-| the error at step n. Try to put, from the condition we cand find n.

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