Vorlesungen

  • Di, 8:15-9:45 (via zoom)
  • Mi, 9:00-9:45 (via zoom; nur CSE)

Übungen

  • Gruppe 1: Mo 10:00-10:45
  • Gruppe 2: Di 10:00-10:45
  • Gruppe 3: Di 10:00-10:45
  • Gruppe 4: Do 10:00-10:45

Vorlesungsfolien

Übungsblätter

Programmteile

  • gauleg.m erzeugt Gaußknoten und Gewichte für die Quadratur auf (-1,1)
  • my_cg.m die klassische CG-Methode

Inhalt (auf Englisch)

  • 5.10.21: Chap. 1.1-1.2: introduction to polynomial interpolation: existence and uniqueness
  • 6.10.21 (CSE): Chap. 1.3: Horner scheme
  • 12.10.21: Chap. 1.4 (Neville scheme), Chap. 1.5 (a simple error estimate for polynomial interpolation) and application to extrapolation of one-sided difference quotients
  • 13.10.21 (CSE): Chap. 1.8 (splines)
  • 19.10.21: Chap. 1.6 (extrapolation of functions with special structure), Chap. 1.7 (Chebyshev interpolation), Chap 2.0 (introduction to numerical integration)
  • 20.10.21 (CSE): Chap. 1.10.1 (trigonometric interpolation)
  • 26.10.21 (postponed to 27.10.21): Chap. 2.1 (Newton Cotes formulas, convergence results for trapezoidal and Simpson rules, Romberg extrapolation)
  • 27.10.21: Chap. 1.10.2 (FFT)
  • 2.11.21 (postponed to 3.11.21): Chap. 2.3 (an adaptive quadrature algorithm), Chap 2.4 (Legendre polynomials and a glance at Gaussian quadrature)
  • 3.11.21 (CSE): Chap. 1.10.3+1.10.4 (applications of FFT like fast multiplication of large numbers)
  • 9.11.21: Chap. 2.5 (comments on trapezoidal rule), 2.6 (quadrature in 2D), Chap. 3 (conditioning and stability)
  • 10.11.21 (CSE) Chap 2.7 (computing Gauss points and weights; Gauss-Jacobi quadrature)
  • 16.11.21 Chap 4.1 (lower and upper triangular matrices), Chap 4.2 (classical Gaussian elimination), Chap 4.3 (LU-factorization via Crout),
  • 17.11.21 (CSE) Chap 4.6 Householder method for QR factorization
  • 23.11.21 Chap 4.4 (Gaussian elimination with pivoting), Chap 4.5 (condition number of a matrix), Chap 5.1 (least squares methods with the method of normal equations)
  • 24.11.21 (CSE) Householder QR-factorization with pivoting, QR-factorization with Givens rotations
  • 30.11.21 Chap 5.2 (least squares methods with QR-factorization), Chap 5.3 (SVD and its properties),
  • 1.12.21 (CSE) Chap 5.3.5 (Moore-Penrose Pseudoinverse)
  • 7.12.21 Chap 6.1 (Newton's method in 1d), Chap 6.2 (convergence of fixed point iterations), Chap 6.3 (Newton's method in multi-d), Chap 6.4 (implementational aspects)
  • 8.12.21 (CSE) Chap 6.7.1 Broyden's method
  • 14.12.21 Chap 6.5.2 (descent methods), Chap 6.5.3 globalized Newton's method, Chap 6.5.4 (Gauss-Newton method)
  • 15.12.21 (CSE) Chap 6.8 (unconstrained minimization problems: gradient methods, trust region methods)
  • 11.1.22 Chap 7.1 (power method), Chap 7.2 (inverse iteration, iteration with shift, Rayleigh quotient iteration), Chap 7.3 (error estimates, stopping criteria)
  • 12.1.22 (CSE) Chap 7.6 (Jacobi method to compute eigenvalues)
  • 18.1.22 Chap 7.4 (orthogonal iteration), chap 7.5 (basic QR algorithm)
  • 19.1.22 (CSE) Chap 7.8 (QR algorithm with shift)

Literatur

  • aktuelle Version des Skriptums (PDF) (wird während des Semesters in unregelmäßigen Abständen aktualisiert)
  • weiterführende Literatur:
    • W. Dahmen, A. Reusken: Numerik für Ingenieure und Naturwissenschaftler
    • Numerical Recipes (Sammlung von C-Routinen für Numerik). Neben den C-Routinen werden die Algorithmen auch kurz "hergeleitet" und beschrieben
    • R. Plato: Numerische Mathematik kompakt (Vieweg)