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ALGORITHMS AND ERRORS

Worksheet 1.1Show your process on each of the following items. Use this worksheet as your answer sheet. Provide extra sheet(s) of paper if needed.

1. Identify the input information, the algorithm and the output information in the problem of

computing the product

2. Compute the product in item 1 using “Russian Peasant Algorithm”.

3. Two lengths and are measured as follows: and where the symbol

representing approximately equal. Compute the approximations

and by “three digit addition”.

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4. The algorithm in item 3 presents errors. Point out the sources of errors and quantify its size.

5. Estimate the errors in output information of item 3 due to the error sources indicated in item 4.

6. Suppose a new theoretical discovery shows that and Recompute items 3 and 5.

7. Find a smaller root of the quadratic equation using three-digit arithmetic.

8. Use the a theoretical concept to compute for the required in item 7.

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