Exercise 4.6-2: Find the optimal value for h that wll minimize the error for the formula f' (xo) ...
More generally, let f(x) be smooth with f"(xo) formula 0. Show that the truncation error in the with hi = h and ho = h/2 must decrease linearly, and not faster, as h → 0.
More generally, let f(x) be smooth with f"(xo) formula 0. Show that the truncation error in the with hi = h and ho = h/2 must decrease linearly, and not faster, as h → 0.
2. Use the centered difference formula to approximate f(z) for f sin and z1, using h 1, 1/10, 1/100, ...., 1 /1015. Plot the absolute error. Explain the behavior as h decreases. (Hint: Read the last subsection of §11 concerning roundoff error.) Why does this instability not arise with -0?
2. Use the centered difference formula to approximate f(z) for f sin and z1, using h 1, 1/10, 1/100, ...., 1 /1015. Plot the absolute error. Explain the behavior as...