From f1cf214cf35b00a61c6e313886c31a8080876a14 Mon Sep 17 00:00:00 2001 From: PolishPigeon Date: Sun, 2 Jan 2022 03:20:22 +0100 Subject: [PATCH] feat: Starting theoretical description project C --- ENUME/projectA/usefullinks.txt | 6 +- .../ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.aux | 18 +-- ...RZYSZTOF_RUDNICKI_307585_ENUME.fdb_latexmk | 26 +++- .../ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.fls | 41 +++++++ .../ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.log | 115 ++++++++++-------- .../ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.pdf | Bin 185325 -> 206214 bytes ...KRZYSZTOF_RUDNICKI_307585_ENUME.synctex.gz | Bin 14533 -> 15886 bytes .../ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.tex | 14 ++- .../ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.toc | 16 +-- 9 files changed, 156 insertions(+), 80 deletions(-) diff --git a/ENUME/projectA/usefullinks.txt b/ENUME/projectA/usefullinks.txt index f34348bf..d9e2b175 100755 --- a/ENUME/projectA/usefullinks.txt +++ b/ENUME/projectA/usefullinks.txt @@ -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.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 diff --git a/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.aux b/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.aux index eaf725ce..cd33fb04 100644 --- a/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.aux +++ b/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.aux @@ -20,15 +20,15 @@ \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline 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\usepackage{mathtools} \usepackage{amsmath} +\usepackage{amsfonts} \usepackage{systeme} \usepackage{siunitx} \usepackage[T1]{fontenc} @@ -38,10 +39,6 @@ linkto=all, } \begin{document} - - - - \maketitle \tableofcontents @@ -79,11 +76,16 @@ $x_i$ & $y_i$ \\ \end{tabular} \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. \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} diff --git a/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.toc b/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.toc index 51fc6576..227ca940 100644 --- a/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.toc +++ b/ENUME/projectC/ENUME_KRZYSZTOF_RUDNICKI_307585_ENUME.toc @@ -1,10 +1,10 @@ \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 {1.2}Theoretical introduction}{2}{section.1.2}% -\contentsline {chapter}{\numberline {2}Determine trajectory of the motion}{3}{chapter.2}% -\contentsline {section}{\numberline {2.1}a) Runge-Kutta method of $4^{th}$ order and Adams PC}{3}{section.2.1}% -\contentsline {subsection}{\numberline {2.1.1}Problem}{3}{subsection.2.1.1}% -\contentsline {subsection}{\numberline {2.1.2}Theoretical Introdution}{4}{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 {subsection}{\numberline {2.2.1}Problem}{4}{subsection.2.2.1}% -\contentsline {subsection}{\numberline {2.2.2}Theoretical Introdution}{4}{subsection.2.2.2}% +\contentsline {section}{\numberline {1.2}Theoretical introduction}{3}{section.1.2}% +\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}{4}{section.2.1}% +\contentsline {subsection}{\numberline {2.1.1}Problem}{4}{subsection.2.1.1}% +\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}{5}{section.2.2}% +\contentsline {subsection}{\numberline {2.2.1}Problem}{5}{subsection.2.2.1}% +\contentsline {subsection}{\numberline {2.2.2}Theoretical Introdution}{5}{subsection.2.2.2}%