Merge branch 'master' of ssh://puls01.eam.uni-erlangen.de:30001/cp1_ws19/exercise_4

instructions/exercise_4.tex

@@ -229,7 +229,7 @@ in your command line/shell before executing your program.
 			\item Calculate the Hesse matrix once and store its value:
 			$$H_k= \nabla^2f(x_k)$$
 			\item Calculate the step size:
-			$$\alpha_k = \frac{\left\langle g_k, d_k\right\rangle}{\left\langle d_k, H_k \cdot d_k\right\rangle}$$
+			$$\alpha_k = -\frac{\left\langle g_k, d_k\right\rangle}{\left\langle d_k, H_k \cdot d_k\right\rangle}$$
 			\item Update the current position:
 			$$x_{k+1} = x_k +\alpha_k \cdot d_k$$
 			\item Calculate the next gradient: 
@@ -241,6 +241,7 @@ in your command line/shell before executing your program.
 		\end{enumerate}
 	\end{enumerate}
 	The resulting $x_n$ is the end approximation of the substep and can afterwards be used as the input for subsequent executions of this subroutine.	 
+	(Consider appropriate conditions to end a loop preliminarily. These may contain: numbers being too small to divide by them, gradients/directional vectors being too short,\ldots)
 	\begin{enumerate}
 		\item In order to structure your code, implement the method \class{ConjugateGradient::CGstep}, which executes one full iteration of the subroutine as detailed above.\\
 		To do that you will need a few extra steps