Solved: Explain-variation of newton method, Engineering Mathematics

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Explain-variation of newton method

Explain the steps on how to solve the problem below:

A) Consider a variation of Newton’s method in which only one derivative is needed; that is x_n+1=x_n-f(x_n)/f′(x₀).Find C and s such that e_n+1=Ce^s_n.

B) Find the conditions on α to ensure that the iteration x_n+1=x_n-af(x_n) will converge linearly (e_n+1≈ 1/2 e_n) to a zero of f if started near the zero.

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Engineering Mathematics: Explain-variation of newton method

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