Q1. Subtractive cancellation occurs when two nearly equal numbers are subtracted. This is a common cause...

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Q1. Subtractive cancellation occurs when two nearly equal numbers are subtracted. This is a common cause of noticeable round-off error. Let's see how this affects numerical differentiation. a) Write a code to approximate the first derivative of f = e* at x = 0 using the forward difference formula (exth - e*)/h with h = 10-, 10-, 10-,..., 10-10. Tabulate the results and true errors. Plot true error vs. h. Comment on the drop rate of the error. b) Repeat part (a) using the central difference formula (exth ex-h)/(2h). Q1. Subtractive cancellation occurs when two nearly equal numbers are subtracted. This is a common cause of noticeable round-off error. Let's see how this affects numerical differentiation. a) Write a code to approximate the first derivative of f = e* at x = 0 using the forward difference formula (exth - e*)/h with h = 10-, 10-, 10-,..., 10-10. Tabulate the results and true errors. Plot true error vs. h. Comment on the drop rate of the error. b) Repeat part (a) using the central difference formula (exth ex-h)/(2h).

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The problem presented is about numerical differentiation and the effects of subtractive cancellation on the accuracy of numerical derivatives Let me walk you through both parts of the question one by ... View the full answer