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Diffstat (limited to 'homeworks/hw-8.tex')
| -rw-r--r-- | homeworks/hw-8.tex | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/homeworks/hw-8.tex b/homeworks/hw-8.tex index 5074689..9071f5b 100644 --- a/homeworks/hw-8.tex +++ b/homeworks/hw-8.tex @@ -1,4 +1,4 @@ -% Created 2023-12-09 Sat 21:43 +% Created 2023-12-09 Sat 22:06 % Intended LaTeX compiler: pdflatex \documentclass[11pt]{article} \usepackage[utf8]{inputenc} @@ -15,10 +15,10 @@ \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry} \author{Elizabeth Hunt} \date{\today} -\title{Homework 7} +\title{Homework 8} \hypersetup{ pdfauthor={Elizabeth Hunt}, - pdftitle={Homework 7}, + pdftitle={Homework 8}, pdfkeywords={}, pdfsubject={}, pdfcreator={Emacs 28.2 (Org mode 9.7-pre)}, @@ -29,11 +29,11 @@ \setlength\parindent{0pt} \section{Question One} -\label{sec:orgb6d5cda} +\label{sec:org800c743} See \texttt{UTEST(jacobi, solve\_jacobi)} in \texttt{test/jacobi.t.c} and the entry \texttt{Jacobi / Gauss-Siedel -> solve\_jacobi} in the LIZFCM API documentation. \section{Question Two} -\label{sec:org9786314} +\label{sec:org6121bef} We cannot just perform the Jacobi algorithm on a Leslie matrix since it is obviously not diagonally dominant - which is a requirement. It is certainly not always the case, but, if a Leslie matrix \(L\) is invertible, we can @@ -53,13 +53,13 @@ but with the con that \(k\) is given by some function on both the convergence cr nonzero entries in the matrix - which might end up worse in some cases than the LU decomp approach. \section{Question Three} -\label{sec:org0ea87d0} +\label{sec:org11282e6} See \texttt{UTEST(jacobi, gauss\_siedel\_solve)} in \texttt{test/jacobi.t.c} which runs the same unit test as \texttt{UTEST(jacobi, solve\_jacobi)} but using the \texttt{Jacobi / Gauss-Siedel -> gauss\_siedel\_solve} method as documented in the LIZFCM API reference. \section{Question Four, Five} -\label{sec:org8eea2ae} +\label{sec:org22b52a9} We produce the following operation counts (by hackily adding the operation count as the last element to the solution vector) and errors - the sum of each vector elements' absolute value away from 1.0 using the proceeding patch and unit test. |