20095ee103_1_hw1_sols

20095ee103_1_hw1_sols - L. Vandenberghe 10/1/09 EE103...

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Unformatted text preview: L. Vandenberghe 10/1/09 EE103 Homework 1 solutions 1. Exercise 1.4. f ( x ) = a T x = a 1 x 1 + + a n x n with a m = 1 1 n , a k = 1 n if k negationslash = m. 2. Exercise 1.5. We first express T as T = a 1 P 1 + a 2 P 2 + a 3 P 3 + b . The four data points give the following information: 10 a 1 + 10 a 2 + 10 a 3 + b = 30 100 a 1 + 10 a 2 + 10 a 3 + b = 60 10 a 1 + 100 a 2 + 10 a 3 + b = 70 10 a 1 + 10 a 2 + 100 a 3 + b = 65 . Subtracting the first equation from the second gives 90 a 1 = 30. Hence, a 1 = 1 / 3. Subtracting the first equation from the third gives 90 a 2 = 40. Hence a 2 = 4 / 9. Subtracting the first equation from the fourth gives 90 a 3 = 35. Hence a 3 = 35 / 90. Plugging in these values in any of the four equations and solving for b gives b = 55 / 3. If all processors operate at the same power P , then T 85 if ( a 1 + a 2 + a 3 ) P + b = 7 6 P + 55 3 85 ....
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20095ee103_1_hw1_sols - L. Vandenberghe 10/1/09 EE103...

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