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Institute of Engineering and Computational Mechanics

Numerical Methods for Analysis and Optimization of Mechanical Systems

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Informations to the Lecture Numerical Methods for Analysis and Optimization of Mechanical Systems:

Summerterm
Dr.-Ing. Florian Fleißner
Prof. Dr.-Ing. Prof. E.h. Peter Eberhard


  • 1. Introduction
  • 2. General principles of numerical calculations
    • 2.1 Definitions
    • 2.2 Numerical principals
    • 2.3 Machine numbers
    • 2.4 Error estimation
  • 3. Systems of linear algebraic equations
    • 3.1 Motivation
    • 3.2 Direct methods for square coefficient matrix
    • 3.3 Cholesky-decomposition
    • 3.4 Gauss-elimination
    • 3.5 LR-decomposition
    • 3.6 QR-decomposition
    • 3.7 Iterative methodes for square coefficient matrix
    • 3.8 Determinant of a matrix
    • 3.9 Matrix inversion
    • 3.10 Least square problem
    • 3.11 Tools and numerical libraries for linear algebraic equations
  • 4. Eigenvalue problems
    • 4.1 General basics
    • 4.2 Normal forms
    • 4.3 Power methods
    • 4.4 QR-algorithm
    • 4.5 Calculation of eigenvectors
    • 4.6 Practical solution of eigenvalue problems
    • 4.7 Tools and numerical libraries for eigenvalue problems
  • 5. Initial value problem for ordinary differantial equations
    • 5.1 Motivation
    • 5.2 Basic remarks>
    • 5.3 Single-step methods
    • 5.4 Extrapolation methods
    • 5.5 Multistep methods
    • 5.6 Comparison of the different methods
    • 5.7 Tools and numerical libraries for initial value problems