mirror of
https://github.com/janishutz/eth-summaries.git
synced 2026-01-11 19:48:27 +00:00
202 lines
9.3 KiB
TeX
202 lines
9.3 KiB
TeX
\documentclass{article}
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\input{~/projects/latex/dist/full.tex}
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\usepackage{lmodern}
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\usepackage{pgfplots}
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\setFontType{sans}
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\renewcommand{\authorTitle}{Robin Bacher, Janis Hutz\\\url{https://github.com/janishutz/eth-summaries}}
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\renewcommand{\authorHeaders}{Robin Bacher, Janis Hutz}
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\setLang{de}
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\setup{Numerical Methods for Computer Science}
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\newcommand{\innumpy}{\fhlc{Cyan}{In \texttt{numpy}}\smallhspace}
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\begin{document}
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\startDocument
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\usetcolorboxes
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\setNumberingStyle{3}
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\setSubsectionNumbering{1}
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% ╭────────────────────────────────────────────────╮
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% │ Title page │
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% ╰────────────────────────────────────────────────╯
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\vspace{2cm}
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\begin{center}
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\begin{tikzpicture}
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\begin{axis}[
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legend pos=outer north east,
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axis lines = box,
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xlabel = size $n$,
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ylabel = Time ($s$),
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variable = t,
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trig format plots = rad,
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]
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\addplot [
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domain=1:10,
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samples=100,
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color=blue,
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]
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{x^2};
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\addlegendentry{$t = n^2$}
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\addplot [
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domain=1:10,
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samples=100,
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color=green,
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]
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{5 * x};
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\addlegendentry{$t = 5n$}
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\addplot [
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domain=1:10,
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samples=100,
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color=red,
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]
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{2^x};
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\addlegendentry{$t = 2^n$}
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\end{axis}
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\end{tikzpicture}
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\end{center}
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\vspace{3cm}
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\begin{center}
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\begin{Large}
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\quote{Wenn ich keine Lust habe, das zu berechnen, dann wende ich einfach Gewalt an}
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\end{Large}
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\hspace{3cm} - Prof. Dr. Vasile Gradinaru, 2025
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\end{center}
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\vspace{2cm}
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\begin{center}
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HS2025, ETHZ\\[0.2cm]
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\begin{Large}
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Summary of the Script and Lectures
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\end{Large}\\[0.2cm]
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\end{center}
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% ────────────────────────────────────────────────────────────────────
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% ╭────────────────────────────────────────────────╮
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% │ Table of Contents │
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% ╰────────────────────────────────────────────────╯
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\newpage
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\printtoc{ForestGreen}
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% ────────────────────────────────────────────────────────────────────
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% ╭────────────────────────────────────────────────╮
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% │ Introduction │
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% ╰────────────────────────────────────────────────╯
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\newpage
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\setcounter{section}{-1}
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\section{Introduction}
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This summary is intended to give you a broad overview of the topics relevant for the exam and is not intended to serve as a full on replacement for the script.
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We have decided to write it in German, as is the new script and for some of the topics that are poorly explained in the script, we have added further explanations.
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The numbering should match the script's numbering exactly (apart from the cases where two definitions were combined due to being closely related and short), making it easier for you to look up the relevant definitions, theorems, etc in context in the script.
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Many of the figures in this summary were taken directly from the Script or Lecture notes created by Professor Vasile Gradinaru.
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We have also taken some explanations and code examples from the slides of our TA, Nils Müller, whose slides can be found
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\color{MidnightBlue}\fbox{\href{https://n.ethz.ch/~muellerni/courses/numcs25.php}{here}}\color{black}
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% TODO: Update this when n.ethz is taken offline completely
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% ────────────────────────────────────────────────────────────────────
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% ╭────────────────────────────────────────────────╮
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% │ Main content │
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% ╰────────────────────────────────────────────────╯
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% ── Introduction ────────────────────────────────────────────────────
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\newsection
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\section{Einführung}
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\input{parts/00_introduction/00_rounding-errors.tex}
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\input{parts/00_introduction/01_time-complexity.tex}
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\input{parts/00_introduction/02_matrix-multiplication.tex}
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% ── polynomial interpolation ────────────────────────────────────────
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\newsection
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\section{Polynominterpolation}
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\input{parts/01_interpolation/00_polynomial/00_intro.tex}
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\input{parts/01_interpolation/00_polynomial/01_monome.tex}
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\input{parts/01_interpolation/00_polynomial/02_newton-basis.tex}
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\input{parts/01_interpolation/00_polynomial/03_lagrange-and-barzycentric-formula.tex}
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\input{parts/01_interpolation/00_polynomial/04_chebyshev-interpolation.tex}
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% ── trigonometric interpolation ─────────────────────────────────────
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\newsection
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\section{Trigonometrische Interpolation}
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\input{parts/01_interpolation/01_trigonometric/00_fourier.tex}
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\input{parts/01_interpolation/01_trigonometric/01_dft/00_intro.tex}
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\input{parts/01_interpolation/01_trigonometric/01_dft/01_construction.tex}
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\input{parts/01_interpolation/01_trigonometric/01_dft/02_fftshift.tex}
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\input{parts/01_interpolation/01_trigonometric/01_dft/03_linalg.tex}
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\input{parts/01_interpolation/01_trigonometric/02_fft.tex}
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\input{parts/01_interpolation/01_trigonometric/03_interpolation/00_intro.tex}
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\input{parts/01_interpolation/01_trigonometric/03_interpolation/01_zero-padding.tex}
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\input{parts/01_interpolation/01_trigonometric/04_error-estimation.tex}
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\input{parts/01_interpolation/01_trigonometric/05_dft-chebyshev.tex}
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% ── piece-wise interpolation ────────────────────────────────────────
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\newsection
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\section{Stückweise Polynomiale Interpolation}
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\input{parts/01_interpolation/02_piece-wise/00_intro.tex}
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\input{parts/01_interpolation/02_piece-wise/01_hermite-interpolation.tex}
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\input{parts/01_interpolation/02_piece-wise/02_splines.tex}
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% ── quadrature ──────────────────────────────────────────────────────
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\newsection
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\section{Numerische Quadratur}
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\input{parts/02_quadrature/00_introduction.tex}
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\input{parts/02_quadrature/01_equidistant-nodes/00_intro.tex}
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\input{parts/02_quadrature/01_equidistant-nodes/01_summed.tex}
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\input{parts/02_quadrature/01_equidistant-nodes/02_romberg-scheme.tex}
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\input{parts/02_quadrature/02_non-equidistant/00_gauss.tex}
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\input{parts/02_quadrature/02_non-equidistant/01_clenshaw-curtis.tex}
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\input{parts/02_quadrature/03_adaptive.tex}
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\input{parts/02_quadrature/04_in-rd.tex}
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\input{parts/02_quadrature/05_monte-carlo.tex}
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\input{parts/02_quadrature/06_reduction-of-variance.tex}
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% ── zeros ───────────────────────────────────────────────────────────
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\newsection
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\section{Nullstellensuche}
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\input{parts/03_zeros/00_intro.tex}
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\input{parts/03_zeros/01_termination-criteria.tex}
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\input{parts/03_zeros/02_fix-point-iteration.tex}
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\input{parts/03_zeros/03_bisection-method.tex}
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\input{parts/03_zeros/04_newton-one-d.tex}
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\input{parts/03_zeros/05_sectant-method.tex}
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\input{parts/03_zeros/06_newton-nd.tex}
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\input{parts/03_zeros/07_damped-newton.tex}
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\input{parts/03_zeros/08_quasi-newton.tex}
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\newsection
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\section{Intermezzo: Lineare Algebra}
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\input{parts/04_linalg/00_intro.tex}
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\input{parts/04_linalg/01_LU.tex}
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\input{parts/04_linalg/02_qr.tex}
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\input{parts/04_linalg/03_svd.tex}
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\newsection
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\section{Ausgleichsrechnung}
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\input{parts/05_curve-fitting/00_intro.tex}
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\input{parts/05_curve-fitting/01_linear/00_intro.tex}
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\input{parts/05_curve-fitting/01_linear/01_normal-equations.tex}
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\input{parts/05_curve-fitting/01_linear/02_orthogonal-transforms.tex}
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\input{parts/05_curve-fitting/01_linear/03_total-curve-fitting.tex}
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\input{parts/05_curve-fitting/02_non-linear/00_intro.tex}
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\input{parts/05_curve-fitting/02_non-linear/01_newton-method-in-rn.tex}
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\input{parts/05_curve-fitting/02_non-linear/02_gauss-newton.tex}
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\input{parts/05_curve-fitting/02_non-linear/03_further-methods.tex}
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\end{document}
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