Consider the following fixed-point iteration: xn+1 = g(xn), where [f(x)] 2 g(x) = x (x +...

 

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Consider the following fixed-point iteration: xn+1 = g(xn), where [f(x)] 2 g(x) = x (x + f(x)) f(x)* (a) What is the order of convergence for the method? (e.g. what is p?). Hint: Show that the method has quadratic convergence. = (b) Perform the fixed-point iteration to find the root of f(x) = x-3x+2. Use xo and the error tolerance = 10-5. Keep at least 6 significant digits in your calculation. -2.2 Consider the following fixed-point iteration: xn+1 = g(xn), where [f(x)] 2 g(x) = x (x + f(x)) f(x)* (a) What is the order of convergence for the method? (e.g. what is p?). Hint: Show that the method has quadratic convergence. = (b) Perform the fixed-point iteration to find the root of f(x) = x-3x+2. Use xo and the error tolerance = 10-5. Keep at least 6 significant digits in your calculation. -2.2