CSE541 Homework #4

Answers

Due Date: Jan. 31

Hardcopy written or typed answers are due at the beginning of class on the due date.
Software (source files and single makefile) is to be submitted (via the 'submit' command) by 3:00 on the due date (before class)

GENERAL INSTRUCTIONS

Homework is due in lecture when I ask for it.
All work must be your own. You are not allowed to work in groups or use third party sources.
Computer problems must be done using C/C++. Turn in a hard copy of your code and print-outs of your sample runs. Please keep this concise, i.e. I don't want you to turn in a lot of pages.
All make-ups for homework must be accompanied by a documented and verifiable excuse well before the deadline. Given the severity of the emergency please inform me as soon as possible.
Please make sure your homework answers are legible, otherwise they will be marked wrong.
Staple your pages.
Homework submissions will NOT be accepted via email to me or the grader. No late homework will be accepted.
For each problem, SHOW ALL WORK in order to receive full credit. Just giving a final answer (correct or incorrect) will receive NO CREDIT. Thus, you will be graded on the work shown.
Each problem is worth the same amount (including the program and associated explanation).
Similarly, each of the n homework assignments will be worth 1/nth of the total for Assignments. 'n' is yet to be determined, but should be around 8.

ASSIGNMENT

Prob. 4.3.3 in book (5th edition)
ans
Prob. 4.8b in book (5th edition)
ans
You are given a program and Makefile that implements differentiation by forward differencing for the function sin(x²). The executable is invoked with command line arguments for the function parameter value, the starting h value and the number of iterations to perform. Each iteration computes an estimate for the derivative at the value using the current value of h, and then divides h by 10 for the next iteration.
As examples, and as part of the assignment, run the Forward Differencing Method (using 'floats') with the following arguments:
```
forward 1.0 0.1 10
central 1.0 0.1 10
Richardson 1.0 0.1 10
```
You are to implement the Central Differencing Method and Richardson Extrapolation (just one level of divided differences).
1. Run these 3 methods using both 'floats' and 'doubles'. Use the results to estimate the best 'h' value for these 6 methods (3 techniques x 2 floating point representations).
2. Rerun these methods at value = 2.0 and again use both 'floats' and 'double'.
Explain the results. Use the 'verbose' mode when appropriate to understand the results. Specifically, what do the results tell you about:
1. the benefit in using smaller values of h in order to get a better approximation to the derivative of a function. At what value of h does the numerator value become totally round-off error?
2. the benefit in using an approximation method with a better error term in order to get a better approximation to the derivative of a function.
3. The tradeoff in using 'double' instead of 'float'.

SPECIFIC INSTRUCTIONS

On the due date, at the beginning of class, hand in hardcopy of

the answers to the problems from the book
your analysis of the results of the lab assignment, including output from the program when and where appropriate.

With respect to the lab assignment,

Electronically 'submit' the makefile and source code files. The assignment is called 'hw4'.
DO NOT SUBMIT THE EXECUTABLE.
Modify the makefile that the grader can use to create your executables. The grader should be able to go into your submit directory, make your executables and then give the commands above:
```
make all
forward 1.0 0.1 10
central 1.0 0.1 10
...
```

NOTES

Anytime you issue 'submit' to an assignment, everything you previously submitted for that assignment is wiped out. That is, you cannot incrementally submit an assignment! Under Unix, you can do a 'man submit' (man is short for 'manual') to get more information about the submit command.
Under UNIX, you can easily make a text file of the output to include, and comment on, with the hardcopy you hand in. For example,
```
ehco "CSE541 Homework #2,  " > output.txt
echo "forward with floats" >> output.txt
forward  1 0.1 10 >> output.txt
...
```
C programming basics
C++ programming basics
sin(x²)