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# hw0 - Homework#0 1 Suppose we have a computer that performs...

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Homework #0 1. Suppose we have a computer that performs 3 digit rounding. What absolute and relative errors do you get for the following numbers and operations performed on that computer: (a) 8 . 1146 (b) 1004 . 21 + 2138 . 6 (c) 4 . 369 · 3 . 4 2. Consider a computer that performs 3 digit rounding for the following: (a) Find an example of positive real numbers a and b such that the floating point representation for a - b has an absolute error 1000. (b) Find an example of positive real numbers c and d such that the floating point representation for c - d has a relative error that exists and is 90%. 3. For the following, work with exact arithmetic: (a) Suppose x = 1 but our approximation is x * = 1 . 001. What are the absolute and relative errors of 10 6 · ( x - 1 . 0005) when using the approximation? (b) Suppose x = 1 but our approximation is x * = 1 . 001. What is the absolute error of the operation 1000000 k =1 x when using the approximation? (c) Suppose x = 1 but our approximation is x * = 1 . 001. Will the relative error of the operation Q n k =1 x become 1000 as n → ∞ when using the approximation?

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hw0 - Homework#0 1 Suppose we have a computer that performs...

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