EB 22, 2018 CSC 349A, 2 1. (a) 12 points) Consider a hypothetical binary computer with an 8-bit normalized, floating- point representation with precision k = 4. If we store the lead 1, what is the largest decimal value we can store? (b) [2 points) Consider the following function f(x) = -T Vr2 0.1 For what values of x may the evaluation of f(x) suffer from subtractive cancellation? Why? (c) [2 points) How many iterations of the bisection method must run to gaurantee that the absolute error of your approximation to the root is less than 10-6 if the initial interval is [0,3]? (a) [4 points) Newton's method with the initial approximation to = 3 will converge to the zero at x = 2 of f(x) = el-2 (14x 12) 7x3 + 20x 26x + 12. Is the order of con- vergence of this computation quadratic? Justify. (DO NOT USE MULTIPLICITY) (a lead I means negative mfan The longest (s 0 0 0 / Se, - 1 C, = 7 e, - OLIV 0 - 2 0 - 3 du jo -6 3) + (7 * 8 EB 22, 2018 CSC 349A, 2 1. (a) 12 points) Consider a hypothetical binary computer with an 8-bit normalized, floating- point representation with precision k = 4. If we store the lead 1, what is the largest decimal value we can store? (b) [2 points) Consider the following function f(x) = -T Vr2 0.1 For what values of x may the evaluation of f(x) suffer from subtractive cancellation? Why? (c) [2 points) How many iterations of the bisection method must run to gaurantee that the absolute error of your approximation to the root is less than 10-6 if the initial interval is [0,3]? (a) [4 points) Newton's method with the initial approximation to = 3 will converge to the zero at x = 2 of f(x) = el-2 (14x 12) 7x3 + 20x 26x + 12. Is the order of con- vergence of this computation quadratic? Justify. (DO NOT USE MULTIPLICITY) (a lead I means negative mfan The longest (s 0 0 0 / Se, - 1 C, = 7 e, - OLIV 0 - 2 0 - 3 du jo -6 3) + (7 * 8