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Advanced Topics in Numerical Analysis I (Winter Semester 2006/07)

Lecture: Wednesday 11:30-13:00 Seminarraum 33
Thursday 9:45-11:15 Seminarraum 11
Problem class: Thursday 14:00-15:30 Neuer Hörsaal
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.

Homework assignments

  • Homework assignment No. 1: PDF
  • Homework assignment No. 2: PDF
  • Homework assignment No. 3: PDF
  • Homework assignment No. 4: PDF
  • Homework assignment No. 5: PDF
  • Homework assignment No. 6: PDF new.jpeg In Problem 21 there is a misprint. It should be: \quad \ldots = w_1f(-1)+w_sf(1)+\sum_{i=2}^{s-1} w_if(x_i)
  • Homework assignment No. 7: PDF
  • Homework assignment No. 8: PDF
  • Homework assignment No. 9: PDF
  • Homework assignment No. 10: PDF
  • Homework assignment No. 11: PDF
  • Homework assignment No. 12: PDF
  • Homework assignment No. 13: PDF
  • Homework assignment No. 14: PDF new.jpeg In Problem 54b) there is a misprint. It should be: \quad \|y(x)-z(x) \|\leq \exp(\rho x)\ldots
  • Homework assignment No. 15: PDF

Programming exercises

  • Programming exercise No. 1: PDF, programming template FFT.C
  • Programming exercise No. 2: PDF
  • Programming exercise No. 3: PDF
  • Programming exercise No. 4: PDF
  • Programming exercise No. 5: PDF


Oral Examinations for Diploma and Master students are offered in the period from the middle of February to the end of April 2007 (Lecture 8 CP and tutorial 2 CP). Registration period from January 26 to February 2, 2007 at the office of W. Müller.


J. Stoer, R. Bulirsch: Introduction to Numerical Analysis (2.ed.), Springer 1996.
W. Gautschi: Numerical Analysis, Birhäuser 1997.
E. Hairer, S.P. Norsett, G. Wanner: Solving Ordinary Differential Equations I, Springer 1993/2000.
L.N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM 1997.