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ESC 251 HW 2 Due: Sep. 1

1)
(6 pt) Consider the list of numbers below:
1.777
 
0.003692
 
113.9
 
0.01992
 
34.39
 
0.5438

a)
What is the exact sum of these numbers?
b)
Add the numbers from largest to smallest using 4 digit chopped arithmetic. What is the relatve error in the result?
c)
Add the numbers from smallest to largest using 4 digit chopped arithmetic. What is the relatve error in the result?
d)
Which of parts b) or c) above gives the most accurate result? Explain why one method has a smaller relative error than the other.
e)
Based on your results, what is the most accurate way to add a series of numbers?
f)
How would your answer to part e) change if you had both positive and negative numbers?

2)
(6 pt) Solve the linear system below using 4 digit, chopped arithmetic. Compute the relative error in the final solution. How does your relative error compare with the examples done in class?


\begin{eqnarray*}
113\,x + 114\,y &=& 1 \\
114\,x + 113\,y &=& -1
\end{eqnarray*}


The exact answer is x = -1, y = 1.

3)
Suppose you have a computer designed with the following specifications: Answer the following questions:
a)
(1 pt) What is the largest positive number that can be represented?
b)
(1 pt) What the smallest positive number that can be represented assuming a standard normalizing rule?
You do not have to convert your numbers to base 10.




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2017-08-30