Let f R R be a given function. The secant method for solving f(x) = 0...

 

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Let f R R be a given function. The secant method for solving f(x) = 0 is a variant of Newton's method. Starting with two initial points To and , we compute a sequence of iterates {n} accoring to the formula In-In-1 In+1=Inf(xn)- n1. f(xn)- f(xn1) Formulate and prove a convergence theorem for the secant method with f(x) = x - 2. Let f R R be a given function. The secant method for solving f(x) = 0 is a variant of Newton's method. Starting with two initial points To and , we compute a sequence of iterates {n} accoring to the formula In-In-1 In+1=Inf(xn)- n1. f(xn)- f(xn1) Formulate and prove a convergence theorem for the secant method with f(x) = x - 2.