Suppose that fl(x) is a k-digit rounding approximation to x. Show that |x - fl(x) X...

 

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Suppose that fl(x) is a k-digit rounding approximation to x. Show that |x - fl(x) X | / S 101-k. Assume that x and x2 are approximations of x and x2, respectively, with relative errors E and E2, and that both of these errors are bounded by E > 0. Moreover, assume that x # x2. Show that x # x2 only if E satisfies 1x - x1 E < |x| + |x| Suppose that fl(x) is a k-digit rounding approximation to x. Show that |x - fl(x) X | / S 101-k. Assume that x and x2 are approximations of x and x2, respectively, with relative errors E and E2, and that both of these errors are bounded by E > 0. Moreover, assume that x # x2. Show that x # x2 only if E satisfies 1x - x1 E < |x| + |x|