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Second Computing Project \\
Math/CS 375, Fall 1997 \\
Professor Coutsias \\
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This project is due Oct. 7. Plan your work
so that if your computer is down a short period, your project will not be late.

This project will count as part of your grade so you must work independently.
It is permissible to discuss the project with your instructor, fellow students,
and friends. However, the computer programs and report must be done only
by the student doing the project.

The project is to use the textbook's procedures Factor and Solve for
solving linear systems and to examine the stability of some problems. 
Specifically, you are asked to:

\begin{enumerate}
\item Find out how to create matrices and vectors using your favorite
language, (f77, c, c++, or Matlab) and how to use Factor and Solve.
\item Use the routines in item 1 to solve systems with the following 
coefficient matrices:
\begin{description}
\item[(i)] $a_{ij} = e^{-(i-j)^{2}}$, $n=8,20$.
\item[(ii)] $a_{ij} = \sin{(ij\pi/(n+1))}$, $n=16$.
\item[(iii)]$a_{ij}=\frac{1}{i+j-1}$, $n=8,20$.
\end{description}
In all cases solve
$Ax=b$ where $b$ is chosen so that the true solution is $x_{i}=1$ for all $i$.
\item
Compute the maximum norm of the error and of the 
residual. Also note the approximate condition number of the matrices as
computed by Factor. Check to see if
the relative errors and residuals satisfy the fundamental inequality derived
in class. 
\end{enumerate}

A well-written description of all your results should be included. Grading 
will approximately follow these guidelines: Correct use of Factor and Solve 
$25\%$, completion of all examples $25\%$, completion of the error analysis
$35\%$, discussion of results $15\%$. 


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