% This is a LaTex file.
% Homework for the course "Iterative Methods for Solving Linear Systems",
% Autumn quarter, 1998, Anne Greenbaum.
% A latex format for making homework assignments.
\documentstyle[12pt]{article}
% The page format, somewhat wider and taller page than in art12.sty.
\topmargin -0.1in \headsep 0in \textheight 8.9in \footskip 0.6in
\oddsidemargin 0in \evensidemargin 0in \textwidth 6.5in
\begin{document}
% Definitions of commonly used symbols.
% The title and header.
\noindent
{\scriptsize Math/AMath 594: Special Topics in Numerical Analysis, Autumn 1998} \hfill
\begin{center}
\large
Assignment 5.
\normalsize
\end{center}
\noindent
Due Wed., Dec. 2.
\vspace{.3in}
% The questions!
\noindent
{\bf Objectives:} To experiment with preconditioners.
\vspace{.3in}
Implement the Incomplete Cholesky and Modified Incomplete Cholesky
preconditioners in your code to solve the diffusion equation (assignment 4).
Take the sparsity pattern of the lower triangular factor to be
the same as that of the lower triangle of $A$.
Again try some different grid sizes (say, $h=1/32$, $h=1/64$, and
$h=1/128$) and see how the number of iterations is related to the
grid size. You might also experiment with some different parameters $\eta$
in the MIC decomposition. [Note: You can check to see if your
IC decomposition is correct by computing the product $L D L^T$ and
making sure that it matches $A$ where $A$ has nonzeros. You can
check your MIC decomposition by making sure that $L D L^T$ matches $A$
where $A$ has nonzero off-diagonal elements and that the row sums
of $L D L^T - (A+E)$ are zero, where $E = \eta h^2 diag(A)$.]
\end{document}