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(c) Apply one iteration of Newton's method with the same starting point and stepsize rule as in (a). How does the cost of the new iterate compare to that obtained in (a)? How about the amount of work involved in finding the new iterate?

1.2.1 Consider the problem of minimizing the function of two variables f(1, y) = 3x + (a) Apply one iteration of the steepest descent method with (1, -2) as the starting point and with the stepsize chosen by the Armijo rule with s = 1, o = 0.1, and 8 = 0.5. (b) Repeat (a) using s = 1, 0 = 0.1, 8 = 0.1 instead. How does the cost of the new iterate compare to that obtained in (a)? Comment on the tradeoffs involved in the choice of B. (c) Apply one iteration of Newton's method with the same starting point and stepsize rule as in (a). How does the cost of the new iterate compare to that obtained in (a)? How about the amount of work involved in finding the new iterate? 1.2.1 Consider the problem of minimizing the function of two variables f(1, y) = 3x + (a) Apply one iteration of the steepest descent method with (1, -2) as the starting point and with the stepsize chosen by the Armijo rule with s = 1, o = 0.1, and 8 = 0.5. (b) Repeat (a) using s = 1, 0 = 0.1, 8 = 0.1 instead. How does the cost of the new iterate compare to that obtained in (a)? Comment on the tradeoffs involved in the choice of B. (c) Apply one iteration of Newton's method with the same starting point and stepsize rule as in (a). How does the cost of the new iterate compare to that obtained in (a)? How about the amount of work involved in finding the new iterate