Lecture: Algorithmics of continuous systems

Summer Term 2015
2015, Apr 10    

Lecturer

Günther Greiner

Teaching Assistents

Matthias Innmann Benjamin Keinert Justus Thies

Content

This lecture introduces a variety of classical algorithms. It covers solvers for linear and non-linear systems, dicretization/quantization, error propagation, interpolation and freeform curves. The following topics are covered in detail:

  • Direct and iterative solvers:
  • LR-,QR-,Cholesky-decomposition
  • SVD
  • Jacobi, Gauss-Seidel iterative solver
  • Newton, Gauss-Newton, Levenberg-Marquardt, etc.
  • linear regression
  • least squares sytems (linear, non-linear)
  • norms
  • Cramer’s rule
  • matrices
  • sparse vs. dense storage (CRS, BCRS, CCS)
  • block matrices (Strassen)
  • parallelization
  • discretization
  • cont. Fourier-Transform
  • sampling theorem (Nyquist-Shannon)
  • aliasing
  • convolutions / filtering
  • error propagation
  • discretization error
  • floating point arithmetic
  • condition (condition number)
  • interpolation
  • 1D / 2D / nD interpolation
  • Bezier curves

Prerequisites

C++, Linear Algebra