Math 370 Fall 98

Quiz 2  Numerical Analysis

Name:

Date:  Wednesday September 9
Time Begun:  Ron Buckmire

Time Ended:

Topic : Implications of Floating Point Arithmetic

The idea behind this quiz is for you to indicate your understanding of how round-off error due to �nite-precision arithmetic crops up in actual computations

Instructions:

1. Once you open the quiz, you have as much time as you need to complete it, but record your start time and end time at the top of this sheet.

2. You may use the book or any of your class notes. You must work alone.

3. If you use your own paper, please staple it to the quiz before coming to class. If you don’t have a stapler, buy one.

4. After completing the quiz, sign the pledge below stating on your honor that you have adhered to these rules.

5. Your solutions must have enough details such that an impartial observer can read your work and determine HOW you came up with your solution.

6. Relax and enjoy...

7. This quiz is due on Monday September 14, in class. NO LATE QUIZZES WILL BE ACCEPTED.

Pledge: I, , pledge my honor as a human being and Occidental student, that I have followed all the rules above to the letter and in spirit.

Math 370 Fall 1998 Quiz 2

SHOW ALL YOUR WORK

1. This problem is �17 on page 28 of Burdern & Faires. Suppose two points (x_{0}, y_{0}) and (x_{1}, y_{1}) are on astraight line with y_{1} ≠ y_{0}. Two formulas are available to �nd the x-intercept of the line:

x_{A} = \frac{x_{0}y_{1} − x_{1}y_{0}}{y_{1} − y_{0}}  and  x_{B} = x_{0} − \frac{(x_{1} − x_{0})y_{0}}{(y_{1} − y_{0})}

a. Show that both formulas are algebraically correct.

b. Use the data (x_{0}, y_{0}) = (1.31, 3.24) and (x_{1}, y_{1}) = (1.93, 4.76) and three-digit rounding arithmetic to compute the x-intercept both ways.

c. Which method is better (formula A or formula B), and why?