fix typos
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@ -1266,5 +1266,5 @@ a collection of pointers of ~Array_int~'s and its dimensions.
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matrix->data[y] = InitArrayWithSize(TYPE, COLS, INIT_VALUE); \
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matrix; \
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})
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#+END_SRc
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#+END_SRC
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Binary file not shown.
@ -1,4 +1,4 @@
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% Created 2023-11-27 Mon 15:18
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% Created 2023-11-29 Wed 18:33
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% Intended LaTeX compiler: pdflatex
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\documentclass[11pt]{article}
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\usepackage[utf8]{inputenc}
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@ -30,7 +30,7 @@
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\setlength\parindent{0pt}
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\section{Design}
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\label{sec:orge377960}
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\label{sec:orge6394d6}
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The LIZFCM static library (at \url{https://github.com/Simponic/math-4610}) is a successor to my
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attempt at writing codes for the Fundamentals of Computational Mathematics course in Common
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Lisp, but the effort required to meet the requirement of creating a static library became
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@ -47,7 +47,7 @@ the C programming language. I have a couple tenets for its design:
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in files, and not individual files per function.
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\end{itemize}
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\section{Compilation}
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\label{sec:orge5bfe63}
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\label{sec:org19eb4ad}
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A provided \texttt{Makefile} is added for convencience. It has been tested on an \texttt{arm}-based M1 machine running
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MacOS as well as \texttt{x86} Arch Linux.
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@ -72,11 +72,11 @@ produce an object file:
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Which is then bundled into a static library in \texttt{lib/lizfcm.a} and can be linked
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in the standard method.
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\section{The LIZFCM API}
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\label{sec:org5e5eaab}
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\label{sec:orgcdad892}
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\subsection{Simple Routines}
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\label{sec:org5dcd9e7}
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\label{sec:org414c16a}
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\subsubsection{\texttt{smaceps}}
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\label{sec:org3672d35}
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\label{sec:org1f871c1}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{smaceps}
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@ -101,7 +101,7 @@ float smaceps() {
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}
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\end{verbatim}
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\subsubsection{\texttt{dmaceps}}
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\label{sec:org2a5eefa}
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\label{sec:orga6517f5}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{dmaceps}
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@ -126,9 +126,9 @@ double dmaceps() {
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}
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\end{verbatim}
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\subsection{Derivative Routines}
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\label{sec:org5d20896}
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\label{sec:org7037c95}
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\subsubsection{\texttt{central\_derivative\_at}}
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\label{sec:org723f321}
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\label{sec:org5004cc1}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{central\_derivative\_at}
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@ -158,7 +158,7 @@ double central_derivative_at(double (*f)(double), double a, double h) {
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}
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\end{verbatim}
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\subsubsection{\texttt{forward\_derivative\_at}}
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\label{sec:orgdeb46bf}
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\label{sec:orgfe0e436}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{forward\_derivative\_at}
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@ -188,7 +188,7 @@ double forward_derivative_at(double (*f)(double), double a, double h) {
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}
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\end{verbatim}
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\subsubsection{\texttt{backward\_derivative\_at}}
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\label{sec:orga47897f}
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\label{sec:orgf50d7e6}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{backward\_derivative\_at}
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@ -218,9 +218,9 @@ double backward_derivative_at(double (*f)(double), double a, double h) {
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}
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\end{verbatim}
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\subsection{Vector Routines}
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\label{sec:org085535d}
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\label{sec:org125771d}
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\subsubsection{Vector Arithmetic: \texttt{add\_v, minus\_v}}
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\label{sec:org1fb6465}
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\label{sec:orgf07f7dd}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{add\_v}, \texttt{minus\_v}
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@ -250,7 +250,7 @@ Array_double *minus_v(Array_double *v1, Array_double *v2) {
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}
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\end{verbatim}
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\subsubsection{Norms: \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}}
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\label{sec:org6fbc1c5}
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\label{sec:org3f50ecb}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}
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@ -283,7 +283,7 @@ double linf_norm(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{vector\_distance}}
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\label{sec:orgc4cd300}
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\label{sec:org77ad0f5}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{vector\_distance}
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@ -303,7 +303,7 @@ double vector_distance(Array_double *v1, Array_double *v2,
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}
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\end{verbatim}
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\subsubsection{Distances: \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}}
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\label{sec:org700af74}
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\label{sec:org83b7946}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}
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@ -328,7 +328,7 @@ double linf_distance(Array_double *v1, Array_double *v2) {
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}
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\end{verbatim}
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\subsubsection{\texttt{sum\_v}}
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\label{sec:org7ff0eaf}
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\label{sec:orgb0e87d6}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{sum\_v}
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@ -346,7 +346,7 @@ double sum_v(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{scale\_v}}
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\label{sec:org6f896b0}
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\label{sec:org08dbec0}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{scale\_v}
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@ -364,7 +364,7 @@ Array_double *scale_v(Array_double *v, double m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{free\_vector}}
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\label{sec:org613ca05}
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\label{sec:org36eb399}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{free\_vector}
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@ -381,7 +381,7 @@ void free_vector(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{add\_element}}
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\label{sec:orga5f01f3}
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\label{sec:org987fa04}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{add\_element}
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@ -400,7 +400,7 @@ Array_double *add_element(Array_double *v, double x) {
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}
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\end{verbatim}
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\subsubsection{\texttt{slice\_element}}
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\label{sec:org7b46996}
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\label{sec:orged034ec}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{slice\_element}
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@ -418,7 +418,7 @@ Array_double *slice_element(Array_double *v, size_t x) {
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}
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\end{verbatim}
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\subsubsection{\texttt{copy\_vector}}
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\label{sec:orgd9c921c}
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\label{sec:org3d6d716}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{copy\_vector}
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@ -437,7 +437,7 @@ Array_double *copy_vector(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{format\_vector\_into}}
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\label{sec:org2ed41e9}
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\label{sec:orgb4ab2db}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{format\_vector\_into}
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@ -466,9 +466,9 @@ void format_vector_into(Array_double *v, char *s) {
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}
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\end{verbatim}
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\subsection{Matrix Routines}
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\label{sec:orgcd9323d}
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\label{sec:orgd984ad2}
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\subsubsection{\texttt{lu\_decomp}}
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\label{sec:org68845f8}
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\label{sec:org184e384}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{lu\_decomp}
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@ -528,7 +528,7 @@ Matrix_double **lu_decomp(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{bsubst}}
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\label{sec:org6362f3f}
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\label{sec:org78c1bb9}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{bsubst}
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@ -553,7 +553,7 @@ Array_double *bsubst(Matrix_double *u, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{fsubst}}
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\label{sec:org214fff4}
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\label{sec:org9d7af79}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{fsubst}
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@ -580,7 +580,7 @@ Array_double *fsubst(Matrix_double *l, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{solve\_matrix\_lu\_bsubst}}
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\label{sec:org37a32e2}
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\label{sec:org85d9237}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -616,7 +616,7 @@ Array_double *solve_matrix_lu_bsubst(Matrix_double *m, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{gaussian\_elimination}}
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\label{sec:orgce10c90}
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\label{sec:orgd188f79}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -671,7 +671,7 @@ Matrix_double *gaussian_elimination(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{solve\_matrix\_gaussian}}
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\label{sec:orgd71062f}
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\label{sec:org2f14966}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -704,7 +704,7 @@ Array_double *solve_matrix_gaussian(Matrix_double *m, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{m\_dot\_v}}
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\label{sec:org4a50148}
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\label{sec:orgc3739fc}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -725,7 +725,7 @@ Array_double *m_dot_v(Matrix_double *m, Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{put\_identity\_diagonal}}
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\label{sec:org6e2b188}
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\label{sec:org6e2dda0}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -743,7 +743,7 @@ Matrix_double *put_identity_diagonal(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{slice\_column}}
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\label{sec:org7a1fa40}
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\label{sec:org6ec00b6}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -766,7 +766,7 @@ Matrix_double *slice_column(Matrix_double *m, size_t x) {
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}
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\end{verbatim}
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\subsubsection{\texttt{add\_column}}
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\label{sec:org6d0a745}
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\label{sec:org46ea124}
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\begin{itemize}
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\item Author: Elizabet Hunt
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\item Location: \texttt{src/matrix.c}
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@ -789,7 +789,7 @@ Matrix_double *add_column(Matrix_double *m, Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{copy\_matrix}}
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\label{sec:org5e29d88}
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\label{sec:org0fb04f5}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -808,7 +808,7 @@ Matrix_double *copy_matrix(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{free\_matrix}}
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\label{sec:org57d90e2}
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\label{sec:org1e7bf4e}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -826,7 +826,7 @@ void free_matrix(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{format\_matrix\_into}}
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\label{sec:orgb0bbd71}
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\label{sec:org7d927f5}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{format\_matrix\_into}
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@ -853,9 +853,9 @@ void format_matrix_into(Matrix_double *m, char *s) {
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}
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\end{verbatim}
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\subsection{Root Finding Methods}
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\label{sec:org48240aa}
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\label{sec:org2d9e027}
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\subsubsection{\texttt{find\_ivt\_range}}
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\label{sec:orgd5ff4a8}
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\label{sec:org13aac0a}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{find\_ivt\_range}
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@ -887,7 +887,7 @@ Array_double *find_ivt_range(double (*f)(double), double start_x, double delta,
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}
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\end{verbatim}
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\subsubsection{\texttt{bisect\_find\_root}}
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\label{sec:org1f1ac63}
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\label{sec:org37c0d43}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{bisect\_find\_root}
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@ -918,7 +918,7 @@ Array_double *bisect_find_root(double (*f)(double), double a, double b,
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}
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\end{verbatim}
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\subsubsection{\texttt{bisect\_find\_root\_with\_error\_assumption}}
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\label{sec:org09bbfc1}
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\label{sec:orga63019e}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{bisect\_find\_root\_with\_error\_assumption}
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@ -946,7 +946,7 @@ double bisect_find_root_with_error_assumption(double (*f)(double), double a,
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}
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\end{verbatim}
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\subsubsection{\texttt{fixed\_point\_iteration\_method}}
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\label{sec:org38792c4}
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\label{sec:org9325db0}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{fixed\_point\_iteration\_method}
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@ -977,7 +977,7 @@ double fixed_point_iteration_method(double (*f)(double), double (*g)(double),
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}
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\end{verbatim}
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\subsubsection{\texttt{fixed\_point\_newton\_method}}
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\label{sec:org019964b}
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\label{sec:orgb571ad9}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{fixed\_point\_newton\_method}
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@ -1005,7 +1005,7 @@ double fixed_point_newton_method(double (*f)(double), double (*fprime)(double),
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}
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\end{verbatim}
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\subsubsection{\texttt{fixed\_point\_secant\_method}}
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\label{sec:org6e9568a}
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\label{sec:org1b33cb8}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{fixed\_point\_secant\_method}
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@ -1032,7 +1032,7 @@ double fixed_point_secant_method(double (*f)(double), double x_0, double x_1,
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}
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\end{verbatim}
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\subsubsection{\texttt{fixed\_point\_secant\_bisection\_method}}
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\label{sec:org44b10fa}
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\label{sec:org9dad67f}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{fixed\_point\_secant\_method}
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@ -1083,9 +1083,9 @@ double fixed_point_secant_bisection_method(double (*f)(double), double x_0,
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}
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\end{verbatim}
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\subsection{Linear Routines}
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\label{sec:orgde42416}
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\label{sec:org89d7d4f}
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\subsubsection{\texttt{least\_squares\_lin\_reg}}
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\label{sec:orgafd3838}
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\label{sec:orgda34435}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{least\_squares\_lin\_reg}
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@ -1115,9 +1115,9 @@ Line *least_squares_lin_reg(Array_double *x, Array_double *y) {
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}
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\end{verbatim}
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\subsection{Eigen-Adjacent}
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\label{sec:org19ad4b1}
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\label{sec:orgc7e86aa}
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\subsubsection{\texttt{dominant\_eigenvalue}}
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\label{sec:orgb93e97e}
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\label{sec:org511efa7}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{dominant\_eigenvalue}
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@ -1161,7 +1161,7 @@ double dominant_eigenvalue(Matrix_double *m, Array_double *v, double tolerance,
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}
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\end{verbatim}
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\subsubsection{\texttt{shift\_inverse\_power\_eigenvalue}}
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\label{sec:orgfa2bf9f}
|
||||
\label{sec:org2f9dea2}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{least\_dominant\_eigenvalue}
|
||||
@ -1209,7 +1209,7 @@ double shift_inverse_power_eigenvalue(Matrix_double *m, Array_double *v,
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsubsection{\texttt{least\_dominant\_eigenvalue}}
|
||||
\label{sec:org06fe228}
|
||||
\label{sec:org847cb9b}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{least\_dominant\_eigenvalue}
|
||||
@ -1227,7 +1227,7 @@ double least_dominant_eigenvalue(Matrix_double *m, Array_double *v,
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsubsection{\texttt{partition\_find\_eigenvalues}}
|
||||
\label{sec:org78fcecb}
|
||||
\label{sec:orgb6cc77c}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{partition\_find\_eigenvalues}
|
||||
@ -1268,7 +1268,7 @@ Array_double *partition_find_eigenvalues(Matrix_double *m,
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsubsection{\texttt{leslie\_matrix}}
|
||||
\label{sec:org8f93a53}
|
||||
\label{sec:org2bb3502}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{leslie\_matrix}
|
||||
@ -1296,12 +1296,12 @@ Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsection{Appendix / Miscellaneous}
|
||||
\label{sec:orgcf92e29}
|
||||
\label{sec:org7ecff9b}
|
||||
\subsubsection{Data Types}
|
||||
\label{sec:org142348e}
|
||||
\label{sec:orgd12d26b}
|
||||
\begin{enumerate}
|
||||
\item \texttt{Line}
|
||||
\label{sec:org8b9b8aa}
|
||||
\label{sec:org5c75544}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/types.h}
|
||||
@ -1314,7 +1314,7 @@ typedef struct Line {
|
||||
} Line;
|
||||
\end{verbatim}
|
||||
\item The \texttt{Array\_<type>} and \texttt{Matrix\_<type>}
|
||||
\label{sec:org4f222f8}
|
||||
\label{sec:orgc595e92}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/types.h}
|
||||
@ -1345,10 +1345,10 @@ typedef struct {
|
||||
\end{verbatim}
|
||||
\end{enumerate}
|
||||
\subsubsection{Macros}
|
||||
\label{sec:orgccc32f4}
|
||||
\label{sec:orgdcaa9de}
|
||||
\begin{enumerate}
|
||||
\item \texttt{c\_max} and \texttt{c\_min}
|
||||
\label{sec:org89ab784}
|
||||
\label{sec:org8f831d6}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
@ -1361,7 +1361,7 @@ typedef struct {
|
||||
#define c_min(x, y) (((x) <= (y)) ? (x) : (y))
|
||||
\end{verbatim}
|
||||
\item \texttt{InitArray}
|
||||
\label{sec:org8113592}
|
||||
\label{sec:org61bb69c}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
@ -1381,7 +1381,7 @@ typedef struct {
|
||||
})
|
||||
\end{verbatim}
|
||||
\item \texttt{InitArrayWithSize}
|
||||
\label{sec:orgf37c5eb}
|
||||
\label{sec:org6bc07d2}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
@ -1401,7 +1401,7 @@ typedef struct {
|
||||
})
|
||||
\end{verbatim}
|
||||
\item \texttt{InitMatrixWithSize}
|
||||
\label{sec:org834639d}
|
||||
\label{sec:orgb5de1b7}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
|
||||
@ -147,7 +147,6 @@ Meaning that as $h$ scales linearly, our error is bounded by $h^2$ as opposed to
|
||||
| 2 | 0.00390625 | 2/9 | 0.22193146 | 0.00029076636 |
|
||||
| 2 | 0.001953125 | 2/9 | 0.22207642 | 0.00014580786 |
|
||||
|
||||
|
||||
* Question Nine
|
||||
** C
|
||||
|
||||
@ -212,7 +211,6 @@ Meaning that as $h$ scales linearly, our error is bounded by $h^2$ as opposed to
|
||||
| 1 | 0.00390625 | 0.41510750774498784d0 | 0.415092913054238d0 | 1.4594690749825112d-5 |
|
||||
| 1 | 0.001953125 | 0.41510750774498784d0 | 0.4150670865046777d0 | 4.0421240310117845d-5 |
|
||||
|
||||
|
||||
* Question Twelve
|
||||
|
||||
First we'll place a bound on $h$; looking at a graph of $f$ it's pretty obvious from the asymptotes that we don't want to go much further than $|h| = 2 - \frac{pi}{2}$.
|
||||
|
||||
20
notes/29-Nov.org
Normal file
20
notes/29-Nov.org
Normal file
@ -0,0 +1,20 @@
|
||||
Jacobi Iteration (cont.)
|
||||
|
||||
x^{k+1} = D^{-1}(b - (L + U)x^k)
|
||||
|
||||
{
|
||||
x^{k+1} = x^k + D^-1 r^k
|
||||
r^{k} = b - Ax^k
|
||||
}
|
||||
|
||||
error: || x^{k+1} - x^k ||_2
|
||||
residual: || r^k ||_2
|
||||
|
||||
Gauss-Seidel Iteration:
|
||||
A = (L + D + U)
|
||||
\Rightarrow Ax = b
|
||||
(D + U)x = b - Lx
|
||||
x = (D + U)^-1 (b - Lx)
|
||||
|
||||
x^{k+1} = (D+U)^{-1}(b - Lx^k)
|
||||
(D + U)^{-1} x (bsubst)
|
||||
2
notes/4-Dec.org
Normal file
2
notes/4-Dec.org
Normal file
@ -0,0 +1,2 @@
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user