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Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ \vspace{0.5em} - \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ \fixme September, 2016} + \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 19 September, 2016} \end{center} \end{frame} } -\begin{frame}\frametitle{Literature} - -\begin{enumerate} -\item J. M. Hammersley, D. C. Hamdscomb, ``Monte Carlo Methods'', London: Methuen \& Co. Ltd., New York: J. Wiley \& Sons Inc., 1964 -\end{enumerate} -\fixme - -\end{frame} \begin{frame}\frametitle{Course plan} \begin{small} diff --git a/Lectures_my/NumMet/Lecture2/mchrzasz.tex b/Lectures_my/NumMet/Lecture2/mchrzasz.tex index ceb7088..1859b4d 100644 --- a/Lectures_my/NumMet/Lecture2/mchrzasz.tex +++ b/Lectures_my/NumMet/Lecture2/mchrzasz.tex @@ -207,7 +207,7 @@ \author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz, Danny van Dyk} (UZH)} \institute{UZH} \title[Function interpolation]{Function Interpolation} -\date{\fixme} +\date{21 September 2016} \begin{document} @@ -242,7 +242,7 @@ \vspace{1em} % \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ \vspace{0.5em} - \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ \fixme September, 2016} + \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 21 September, 2016} \end{center} \end{frame} } @@ -259,7 +259,7 @@ $f_i=f(x_i)$ & $f_1$ & $f_2$ & $f_3$ & ... & $f_n$ \\ \end{tabular}\\ \ARROWR The $x_i$ are data points.\\ -\ARROW The problem is how to calculate the function values between the points ({\it intepolation}) or outside ({\it extrapolation}). +\ARROW The problem is how to calculate the function values between the points ({\it interpolation}) or outside ({\it extrapolation} - see next lecture!) . \end{small} \begin{center} \includegraphics[angle=-90,width=0.5\textwidth]{images/mass_resolution_Bconstr_afterSel_errBand_scaled.pdf} @@ -356,8 +356,8 @@ \begin{align*} \psi_0=1,~~~\psi_1=x,~~~\psi_2=x^2,~~~...~~~, \psi_n=x^n \end{align*} -\begin{alertblock}{Attention/Ahtung:} -This kind of interpolation is wrongly conditioned: small changed of input parameters will cause large output differences. +\begin{alertblock}{Attention/Achtung:} +This kind of interpolation is wrongly conditioned: small changes of input parameters will cause large output differences. \end{alertblock} \ARROW Because of the above it is used almost not used in practice. \\ @@ -581,12 +581,12 @@ -\begin{frame}\frametitle{First degree splain function} +\begin{frame}\frametitle{First degree spline function} \begin{small} \ARROW Till now using couple numerical methods we were able to calculate coefficients of a big single polynomial equation.\\ \ARROW Now we are smarter then Newton and Lagrange were over 300 years ago!\\ -\ARROW We can use several interpolating functions and then glue them (splain) them together!\\ +\ARROW We can use several interpolating functions and then glue them (splice) them together!\\ \ARROW In order to do so we divide the domain of the $F$ function $\left[ a,b \right]$ into: \begin{align*} a=x_0