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\title{Homework Extra}

\input{preamble.tex}
\title{Homework}



\begin{document}
\maketitle

Please answer the following questions in complete sentences by Thursday,
2016-12-15 at 3pm.

\section{Homework Extra}\label{homework-extra}

My policy on these questions is different from the usual homework
grading. I will tend to give one of three scores: full points, half
points or zero points.

A full points solution will be a well-articulated, well presented
solution that gets at all the important and relevant issues.

A half points solution is correct, but is lacking in presentation
details and/or misses a minor aspect of the problem.

A zero point solution may get some ideas or pieces of the solution right
but is missing major components.

In order words, don't do the extra credit unless you want to do a good
job at writing up and presenting the solution. It will not be easy to
get full points and I will be picky.

\subsection{Problem 0: Collaboration}\label{problem-0-collaboration}

There is no collaboration allowed on this assignment. None, nada, zero.
You must answer the following question, which is worth one point,
multiplicatively applied on your entire extra credit. There is only one
acceptable answer.

Please report the people you worked with on this assignment.

\subsection{Problem 1: Boundary value problems (20
points)}\label{problem-1-boundary-value-problems-20-points}

Complete all parts of Chapter 13, Problem 2 in Julia.

\subsection{Problem 2: A tridiagonal solver (20
points)}\label{problem-2-a-tridiagonal-solver-20-points}

Consider a system of linear equations $\mA \vx = \vb$ where $\mA$ is
tridiagonal: \[ \mA = \bmat{A_{11} & A_{12} & 0 & \ldots & 0 \\
               A_{21} & A_{22} & A_{23} & \ddots & \vdots \\
               0 & A_{32} & \ddots & \ddots & \vdots \\
               \vdots & \ddots & \ddots & \ddots & A_{n-1,n} \\
                0 & \ldots & 0 & A_{n,n-1} & A_{n,n}  } \]

Describe, develop, implement, and test a piece of software to solve
these systems of equations using LU with partial pivoting in time that
is $O(n)$, where $n$ is the dimension of the system. Your solver should
be well documented so that it is clear how your code maps to your
algorithm and also how I would use your code.

This problem must include an ipython notebook or julia file that will
reproduce your timing results on a new computer that I can run for
myself.

\subsection{Problem 3: Polynomial Interpolation (20
points)}\label{problem-3-polynomial-interpolation-20-points}

Write a Julia program that will output nicely formatted LaTeX
representations of the Lagrange interpolating polynomial as $O(n^2)$
terms and the monomial representation of that same interpolating
polynomial.

Find a 30 to 50 point set of data with 5-6 digits used for each number
and show your results. Your data should be compelling.

\end{document}
