MACM 316 ASSIGNMENT #2 Quiz on Friday, May 28, 2021 Reading: Section 2.1-2.2 in the textbook. 1. Compute the machine epsilon (as real decimal numbers) in the following floating point systems for both rounding and choping. a). Base 10 with 3-digit mantissa. b). Base 2 with 2-digit mantissa. c). Base 7 with 1-digit mantissa. 2. In the floating point systems with base 10 and 1-digit mantissa using rounding a). Compute √ x+ 2−√x for x = 528. b). Compute √ x+ 2−√x for x = 528 without using subtraction. 3. Check that the recurrence xn+1 = (2xn−1 − 5xn) 3 with initial values x0 = 1 and x1 = 1 3 gives the sequence xn = ( 1 3 )n . 4. Note that 13 = 0.3333... and machines can only store finite digits, so 1 3 is 1 3 − in machines, while 1 is just 1 in machines. Plug y0 = 1 and y1 = 13− in the recurrence yn+1 = (2yn−1 − 5yn) 3 and compute y2, y3 and y4. Compute the absolute errors between y2, y3, y4 and 1 32 , 1 33 , 1 34 respectively. 1

















































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