Assume we are using the forward difference formula to compute the derivative of

Question

Assume we are using the forward difference formula to compute the derivative of the function f(x) = x2 - 5, at the point x = 3,  using a step size of 0.0001. Assume we are using single precision to store our numbers. What type of error is dominating and what should we do to minimize the total error in the derivative?

Select one:

a. Round-off error dominates, and we should increase the step size to decrease the error.

b. Round-off error dominates, and we should reduce the step size to decrease the error.

c. Truncation error dominates, and we should reduce the step size to decrease the error.

d. Truncation error dominates, and we should increase the step size to decrease the error.

Explanation / Answer

(Single precision) E_T 10^(-7) &
(Forward Difference) E_T o(h)

As 0.0001 >>  than E_T 10^(-7) than we can state that the truncation error will dominate the derivative. And to minimize the error we need to decrease the step size.

So correct option is

c. Truncation error dominates, and we should reduce the step size to decrease the error.

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