CS 3414 Homework 1
Due 5:00 p.m., May 29, 2002

  1. Problem 38 on page 71 of Cheney and Kincaid.

  2. Problem 42 on page 72 of Cheney and Kincaid.

  3. Assuming 3 decimal digit rounded arithmetic at every step, add up the following numbers in increasing order and then in decreasing order.
        639., 412., 22.7, 4.35
    Compute the relative error in the final answer in each case. Which approach is better and why? (Note that `relative error' means relative to the true answer.)

  4. Run the two C programs prog1.c and prog2.c on a machine of your choice. Summarize and discuss the results. What two quantities properties to the underlying floating point representation scheme are estimated by these two programs? Do not turn in a copy of the programs or of the entire output. Do give enough details describing what happens to convince the reader that you ran the programs and thought about the results. Be sure to indicate the type of system you ran the codes on, i.e., processor (if you know it), operating system, and compiler.

  5. Problem 8 on page 99 of Cheney and Kincaid. Show a little work.

  6. Problem 23 on page 115 of Cheney and Kincaid.

  7. Problem 25 on page 115 of Cheney and Kincaid. To find the number of iterations needed to obtain 10-6 accuracy, just run versions of the algorithms. (See the on-line repository of codes associated with our text here.)

  8. Solve the early retirement problem described here. (Start with one of the codes available in the on-line repository of codes associated with our text.) Turn in a neat summary of the results and attach a copy of your code. Your summary of results should simply be a table like this:
        Year     4.0%      4.5%      5.0%      5.5%      6.0%
        2003   2584.55