\section{Results}
\subsection{Starting matrix}
I decided to generate random symmetric matrix using following code:
\hyperlink{function4_matrix_generation}{code for matrix generation.}
I got the following matrix:
\[
\begin{bmatrix}
171  &  48  & 133  &  81  &  93 \\
 48  & 108  &  63  &  35  &  30 \\
133  &  63  & 131  &  64  &  91 \\
 81  &  35  &  64  &  41  &  37 \\
 93  &  30  &  91  &  37  & 106
\end{bmatrix}
\]

Putting it through Matlab eig function I got eigen values equal to:
\[
10^{2} *
\begin{bmatrix}
  0.000050598692964 \\
  0.105696602175690 \\
  0.454589544003707 \\
  0.870708987227002 \\
  4.138954267900641
\end{bmatrix}
\]

\newpage
\subsection{QR method with no shifts}
Putting this matrix to my functions QRNoShifts and QRShifts I got:
for qr method with no shifts:
Final matrix:
\[
\begin{bmatrix}
413.8954  &  0.0000  & -0.0000  &  0.0000  &  0.0000 \\
 0.0000  & 87.0709  &  -0.0000  &  -0.0000  &  0.0000 \\
0.0000  &  -0.0000  & 45.4590  &  -0.0000  &  -0.0000 \\
 -0.0000  &  0.0000  &  -0.0000  &  10.5697  &  -0.0000 \\
 0.0000  &  -0.0000  &  0.0000  &  0  & 0.0051
\end{bmatrix}
\]

Eigen values:
\[
10^{2} *
\begin{bmatrix}
  4.138954267900639 \\
   0.870708987227001 \\
   0.454589544003706 \\
   0.105696602175689 \\
   0.000050598692964 \\
\end{bmatrix}
\]

It took \textbf{26} iterations to get those values.

\subsection{QR method with shifts}
For qr method with shiftts:
Final matrix:
\[
\begin{bmatrix}
413.8954
\end{bmatrix}
\]

Eigen values:
\[
10^{2} *
\begin{bmatrix}
  0.454589544003706 \\
  0.870708987227001 \\
  0.105696602175689 \\
  0.000050598692964 \\
  4.138954267900639
\end{bmatrix}
\]

It took \textbf{12} iterations to get those values.

\newpage