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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2024--25--B term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Approximation Theory

  \item[Course Number]
    \LRE{201‭.1‭.0121}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il//en/teaching/spring2025/courses/approximation-theory}

  \item[Lecturer]
    Prof. Amnon Besser,
    \nolinkurl{<bessera@bgu.ac.il>},
    Office 212

\item[Office Hours]
  \url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

\begin{enumerate}
\item{} Preliminaries: floating point arithmetic, round-off errors and stability. Matrix norms and the condition number of a matrix.
\item{} Introduction to numerical solutions for ODE's:initial value problems, Euler's method, introduction to multistep methods. Boundary value problems.
\item{} Numerical solution of linear equations: Gauss elimination with pivoting, LU decomposition. Iterative techniques: Jacobi, Gauss-Seidel, conjugate gradient. Least squares approximation.
\item{} Numerical methods for finding eigenvalues: Gershgorin circles. The power method. Stability considerations in Gram-Schmidt: Hausholder reflections and Givens rotations. Hessenberg and tridiagonal forms. QR decomposition and the QR algorithm.
\end{enumerate}

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\end{document}

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