CSE541 Homework #2

Answers

Due Date:

Hardcopy written or typed answers are due at the beginning of class, Thursday, Jan. 19 in class
Software (source files and single makefile) is to be submitted (via the 'submit' command) by 3:00 on Thursday, Jan. 19 (before class)

FINALIZED

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), in this case 1/4 of this homework assignment.
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

You are given a program that implements a simple bisection method in order to compute the square root of 2. The executable is invoked with command line arguments for the low and high bracketing values and the number of iterations.
As examples, and as part of the assignment, run the Bisection Method with the following arguments.
```
bisection 1 2 20
bisection 1 5 20
bisection 1 10 20
```
You are to implement the Regula Falsi Method. If you have limited programming experience, I suggest you make a copy of the Bisection Method code and modify it, keeping the same program structure. If you are a more experienced programmer, you are free to program this up from scratch any way you want as long as the compilation via a makefile and the execuation still adhere to the assignment requirements. See below on how to submit the source codes and makefile for the solution methods.
Run the regulaFalsi method with the following arguments:
```
regulaFalsi 1 2 20
regulaFalsi 1 5 20
regulaFalsi 1 10 20
```
Explain the results of both the Bisection Method and the Regula Falsi Method in the hardcopy you hand in at the beginning of class on the due day. Compare the output of the Bisection Method and the Regula Falsi Method. Use sketches showing how the algorithms solve the problem where appropriate and explain how one outperforms the other for given input.
In the code for the Regula Falsi Method, change the 'Real float' line to 'Real double' and re-execute the 3 runs. Explain the results. Compare the output of the Regula Ralsi Method runs that use doubles to the runs that use floats and discuss the results.
Code up and run Newton's Method for the same problem (using 'floats). Use the following:
```
Newton 1 10
```
Note the value of the error when using starting point of '1'. Use 'verbose' mode to see the convergence. Find low and high values for the starting point where the error significantly changes (say, a couple orders of magnitude). Briefly discuss how Newton's Method solves this problem for a wide range of values (draw a diagram).
Code up and run the Secant Method for the same problem (using 'floats). Use the following:
```
secant 0.5 0.55 10

secant 0.5 0.6 10
```
Use verbose mode to see the convergence. Discuss the results and any difference you see.

SPECIFIC INSTRUCTIONS

The assignment is called 'hw2'.

Create a makefile that the grader can use to create your executables. The makefile, for example, can look like:

all: bisection regulaFalsi Newton secant

bisection: bisection.c
       gcc -lm bisection.c -o bisection

regulaFalsi: regulaFalsi.c
       gcc -lm regulaFalsi.c -o regulaFalsi

Newton: Newton.c
       gcc -lm Newton.c -o Newton

secant: secant.c
       gcc -lm secant.c -o secant

clean:
       rm bisection regulaFalsi Newton secant

DO NOT SUBMIT THE EXECUTABLE. The grader should be able to go to your submit directory to compile your program with:

make all

and then issue the commands as in the assignment above.

There is also amble makefile information on the web, such as this Makefile tutorial.

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 "problem 1" >> output.txt
bisection 1 2 20 >> output.txt
bisection 1 5 20 >> output.txt
bisection 1 10 20 >> output.txt
echo " " >> output.txt
echo "problem 2" >> output.txt
regulaFalsi 1 2 20 >> output.txt
...

C programming basics
C++ programming basics