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feat: Starting theoretical description project C

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PolishPigeon 2022-01-02 03:20:22 +01:00
parent 679ae2635c
commit f1cf214cf3
9 changed files with 156 additions and 80 deletions
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6
ENUME/projectA/usefullinks.txt
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@ -57,4 +57,8 @@ https://tex.stackexchange.com/questions/294561/using-textbf-vs-mathbf-in-math-mo
https://www.math-linux.com/latex-26/faq/latex-faq/article/how-to-get-dots-in-latex-ldots-cdots-vdots-and-ddots - Dots LaTeX https://www.math-linux.com/latex-26/faq/latex-faq/article/how-to-get-dots-in-latex-ldots-cdots-vdots-and-ddots - Dots LaTeX
https://www.overleaf.com/learn/latex/Tables - Tables LaTeX https://www.overleaf.com/learn/latex/Tables - Tables LaTeX
https://en.wikibooks.org/wiki/LaTeX/Special_Characters - an arrow (circumflex) above letter in latex
https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols - For every symbol in LaTeX

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ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.aux
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ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.tex
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@ -2,6 +2,7 @@
\usepackage{mathtools} \usepackage{mathtools}
\usepackage{amsmath} \usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{systeme} \usepackage{systeme}
\usepackage{siunitx} \usepackage{siunitx}
\usepackage[T1]{fontenc} \usepackage[T1]{fontenc}
@ -38,10 +39,6 @@ linkto=all,
} }
\begin{document} \begin{document}
\maketitle \maketitle
\tableofcontents \tableofcontents
@ -79,11 +76,16 @@ $x_i$ & $y_i$ \\
\end{tabular} \end{tabular}
\end{center} \end{center}
We have to determine polynomial function $ y = f(x) $ that best fits this data. We have to determine polynomial function $ y = f(x) $ that best fits this data. \\
We will use least-square approximation using system of normal equation with QR factorization. We will use least-square approximation using system of normal equation with QR factorization.
\section{Theoretical introduction} \section{Theoretical introduction}
We have polynomial function:
\[ y(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x^1 + a_0 \]
where n - degree of the polynomial we use to approximate function \\
Given matrix $\mathbf{A} \in \mathbb{R}^{m \times n} \quad (m > n)$ and vector $\mathbf{y} \in \mathbb{R}^m$ \\
We need to find vector \^{x} such that:
\[ \forall x \in \mathbb{R}^n \quad|| \mathbf{y} - \mathbf{A} \hat{x} ||_2 \leq || \mathbf{y} - \mathbf{A}x ||_2 \]
\chapter{Determine trajectory of the motion} \chapter{Determine trajectory of the motion}

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ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.toc
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\contentsline {chapter}{\numberline {1}Determine polynomial function fitting experimental data}{2}{chapter.1}% \contentsline {chapter}{\numberline {1}Determine polynomial function fitting experimental data}{2}{chapter.1}%
\contentsline {section}{\numberline {1.1}Problem}{2}{section.1.1}% \contentsline {section}{\numberline {1.1}Problem}{2}{section.1.1}%
\contentsline {section}{\numberline {1.2}Theoretical introduction}{2}{section.1.2}% \contentsline {section}{\numberline {1.2}Theoretical introduction}{3}{section.1.2}%
\contentsline {chapter}{\numberline {2}Determine trajectory of the motion}{3}{chapter.2}% \contentsline {chapter}{\numberline {2}Determine trajectory of the motion}{4}{chapter.2}%
\contentsline {section}{\numberline {2.1}a) Runge-Kutta method of $4^{th}$ order and Adams PC}{3}{section.2.1}% \contentsline {section}{\numberline {2.1}a) Runge-Kutta method of $4^{th}$ order and Adams PC}{4}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}Problem}{3}{subsection.2.1.1}% \contentsline {subsection}{\numberline {2.1.1}Problem}{4}{subsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1.2}Theoretical Introdution}{4}{subsection.2.1.2}% \contentsline {subsection}{\numberline {2.1.2}Theoretical Introdution}{5}{subsection.2.1.2}%
\contentsline {section}{\numberline {2.2}b) Runge-Kutta method of $4^{th}$ order with variable step size automatically adjusted}{4}{section.2.2}% \contentsline {section}{\numberline {2.2}b) Runge-Kutta method of $4^{th}$ order with variable step size automatically adjusted}{5}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}Problem}{4}{subsection.2.2.1}% \contentsline {subsection}{\numberline {2.2.1}Problem}{5}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2.2.2}Theoretical Introdution}{4}{subsection.2.2.2}% \contentsline {subsection}{\numberline {2.2.2}Theoretical Introdution}{5}{subsection.2.2.2}%