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Numerische Mathematik II (Winter Semester 2006/07)

  • Lecturer: Prof. Dr. Rudolf Scherer
  • Classes: Lecture (1085), Problem class (1087)
  • Weekly hours: 4+2
  • Audience: math (5.-7. semester)
Lecture: Wednesday 8:00-9:30 Neuer Hörsaal Begin: 25.10.2006, End: 15.2.2007
Thursday 8:00-9:30 Neuer Hörsaal
Problem class: Thursday 14:00-15:30 Neuer Hörsaal Begin: 26.10.2006, End: 15.2.2007
Lecturer Prof. Dr. Rudolf Scherer
Office hours: by appointment (via Email)
Room 0.011 Kollegiengebäude Mathematik (20.30)
Email: rudolf.scherer@kit.edu
Problem classes Dr. Wolfgang Müller
Office hours:
Room Allianz-Gebäude (05.20)
Email: wolfgang.mueller@kit.edu


This course investigates the following advanced topics:

I. Interpolation, Approximation and Quadrature: Interpolation problem, trigonometric interpolation, Fourier transformation, fast Fourier transform (FFT), spline interpolation, Gaussian quadrature formulas, extrapolation methods.

II. Eigenvalue Problems of Matrices: Localisation and estimation of eigenvalues, symmetric tridiagonal matrices, reduction methods of Householder, methods of Givens and Jacobi, vector iteration method, LR and QR methods.

III. Numerical Solution of Ordinary Differential Equations: Initial value problems, boundary value problems, discretization methods, Runge--Kutta methods, linear multistep methods, order of consistency, convergence and asymptotic stability, absolute stability, boundary value problem of Sturm, shooting method.


J. Stoer, R. Bulirsch: Einführung ind die Numerische Mathematik II (4.ed.), Springer 2000.
E. Hairer, S.P. Norsett, G. Wanner: Solving Ordinary Differential Equations I, Springer 1993/2000.
H.R. Schwarz, Numerical analysis. A comprehensive introduction. With a contribution by J. Waldvogel.
Chichester: John Wiley & Sons, 1989.
P. Deuflhard, A. Hohmann, Numerical analysis in modern scientific computing. An introduction.
(2nd revised ed.) New York, NY: Springer, 2003.

Further information

Homework assingments, programming execises and further information in English can be found here.