diff --git a/semester3/numcs/parts/01_interpolation/01_trigonometric/02_fft.tex b/semester3/numcs/parts/01_interpolation/01_trigonometric/02_fft.tex index 6a99cd1..2b38de8 100644 --- a/semester3/numcs/parts/01_interpolation/01_trigonometric/02_fft.tex +++ b/semester3/numcs/parts/01_interpolation/01_trigonometric/02_fft.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \newsection \subsection{Schnelle Fourier Transformation} Da es viele Anwendungen für die Fourier-Transformation gibt, ist ein Algorithmus mit guter Laufzeit sehr wichtig. diff --git a/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/00_intro.tex b/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/00_intro.tex index 90e1991..4cd7273 100644 --- a/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/00_intro.tex +++ b/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/00_intro.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \newsection \subsection{Trigonometrische Interpolation} \subsubsection{Von Approximation zur Interpolation} diff --git a/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/01_zero-padding.tex b/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/01_zero-padding.tex index 91b04af..10cdc27 100644 --- a/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/01_zero-padding.tex +++ b/semester3/numcs/parts/01_interpolation/01_trigonometric/03_interpolation/01_zero-padding.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \newpage \subsubsection{Zero-Padding-Auswertung} Ein trigonometrisches Polynom $p_{N - 1}(t)$ kann effizient an den äquidistanten Punkten $\frac{k}{M}$ mit $M > N$ ausgewertet werden, für $k = 0, \ldots, M - 1$. diff --git a/semester3/numcs/parts/01_interpolation/01_trigonometric/04_error-estimation.tex b/semester3/numcs/parts/01_interpolation/01_trigonometric/04_error-estimation.tex index b611a9a..199dec0 100644 --- a/semester3/numcs/parts/01_interpolation/01_trigonometric/04_error-estimation.tex +++ b/semester3/numcs/parts/01_interpolation/01_trigonometric/04_error-estimation.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \newsection \subsection{Fehlerabschätzungen} diff --git a/semester3/numcs/parts/01_interpolation/01_trigonometric/05_dft-chebyshev.tex b/semester3/numcs/parts/01_interpolation/01_trigonometric/05_dft-chebyshev.tex index 9ee80c8..f8baa2e 100644 --- a/semester3/numcs/parts/01_interpolation/01_trigonometric/05_dft-chebyshev.tex +++ b/semester3/numcs/parts/01_interpolation/01_trigonometric/05_dft-chebyshev.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \newsection \subsection{DFT und Chebyshev-Interpolation} Mithilfe der DFT können günstig und einfach die Chebyshev-Koeffizienten ($c_k$) berechnet werden. diff --git a/semester3/numcs/parts/01_interpolation/02_piece-wise/00_intro.tex b/semester3/numcs/parts/01_interpolation/02_piece-wise/00_intro.tex index 7cf74b3..cbfb430 100644 --- a/semester3/numcs/parts/01_interpolation/02_piece-wise/00_intro.tex +++ b/semester3/numcs/parts/01_interpolation/02_piece-wise/00_intro.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + % Lecture: \chi here are used as RELU function! \subsection{Stückweise Lineare Interpolation} Globale Interpolation (also Interpolation auf dem ganzen Intervall $]-\infty, \infty[$) funktioniert nur dann gut, wenn: diff --git a/semester3/numcs/parts/01_interpolation/02_piece-wise/01_hermite-interpolation.tex b/semester3/numcs/parts/01_interpolation/02_piece-wise/01_hermite-interpolation.tex index 970adc2..4d4f71b 100644 --- a/semester3/numcs/parts/01_interpolation/02_piece-wise/01_hermite-interpolation.tex +++ b/semester3/numcs/parts/01_interpolation/02_piece-wise/01_hermite-interpolation.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \subsection{Kubische Hermite-Interpolation} Die Kubische Hermite-Interpolation (CHIP) produziert eine auf $[a, b]$ stetig differenzierbare Funktion, welche auf den Teilintervallen $[x_{j - 1}, x_j]$ jeweils ein Polynom von Grad 3 ist. Wichtige Eigenschaft von Polynomen $n$-ten Grades ist, dass sie $n + 1$ Freiheitsgrade haben (da sie $n + 1$ freie Variabeln enthalten). diff --git a/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex b/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex index 134da3d..f095bce 100644 --- a/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex +++ b/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \newsectionNoPB \subsection{Splines} \begin{definition}[]{Raum der Splines} diff --git a/semester3/numcs/parts/02_quadrature/00_introduction.tex b/semester3/numcs/parts/02_quadrature/00_introduction.tex index c8aae13..a6f10d0 100644 --- a/semester3/numcs/parts/02_quadrature/00_introduction.tex +++ b/semester3/numcs/parts/02_quadrature/00_introduction.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ AUTHOR: Janis Hutz │ +% └ ┘ + \setcounter{subsection}{2} \subsection{Grundbegriffe und -Ideen} Es ist oft nicht möglich oder sinnvoll einen Integral analytisch zu berechnen. diff --git a/semester3/numcs/parts/02_quadrature/01_equidistant-nodes.tex b/semester3/numcs/parts/02_quadrature/01_equidistant-nodes.tex index 595128a..d837bcf 100644 --- a/semester3/numcs/parts/02_quadrature/01_equidistant-nodes.tex +++ b/semester3/numcs/parts/02_quadrature/01_equidistant-nodes.tex @@ -1,3 +1,7 @@ +% ┌ ┐ +% │ Author: Robin Bacher │ +% └ ┘ + \newsection \subsection{Äquidistante Punkte} \label{sec:equidistant-nodes}