Numerical Methods

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Numeriske Metoder / Numerical methods. F08

[ FAQ | Pensum | Homeworks | F06 home-page ]

NB:

Karaktererne findes der nede i tabellet. I har 24 time for at klage... :)
Fristen udsættes til Juni d. 23. kl. 24:00. Er I sikre på, at det er nok?
Husk chmod --recursive +xr ~/public_html
An example of using the unix graph utility is here.
An example of using the gnuplot utility is here

Schedule:

Lectures: Tirsdag, 11:15, 1520-616; Onsdag, 14:15, 1520-616

Exercises: Hold 1: Torsdag, 11:15 i 1525-319; Hold 2: Fredag, 12:15 i 1525-319

Exercises:

Hello World, QR-decomposition, Eigenvalues, Least-Squares fit, Interpolation, RootFinding and Optimization, ODEs, Adaptive integration, Monte Carlo integration, FFT,

Weekly notes:

[png-1, png-2; pdf] Systems of linear equations: QR-decomposition and back-substitution; determinant of a matrix; matrix inverse.
[png-1, png-2; pdf] Eigenvalues and eigenvectors: Jacobi transformation; QR algorithm; inverse iteration.
[png-1, png-2; pdf] Linear least-squares problem; least-squares solution with QR-method; linear least-squares fit; errors and covariance matrix.
[png-1, png-2; pdf] Interpolation: polynomial interpolation; spline interpolation.
[png-1, png-2; pdf] Nonlinear equations and optimization: modified Newton method; downhill simplex method.
[png-1, png-2; pdf] Ordinary differential equations: one-step, multi-step, predictor-corrector methods; estimation of errors, adaptive step-size strategy.
[png-1, png-2; pdf] Numerical integration: quadratures with optimized abscissas (Gauss); quadratures with equally spaced abscissas (Newton-Cotes); adaptive algorithm with equally spaced abscissas; Gauss-Kronrod quadratures.
[png-1, png-2; pdf] Monte Carlo integration: plain Monte Carlo; importance sampling; stratified sampling; quasi-random sequences.
[png, pdf] Fast Fourier transform
Ideas for projects:
- [ png, pdf; see also this preprint ] Feynman path integral for one-dimensional oscillator;
- [ png, pdf] Calculations of the (complex) special functions.

Literature:

Numerical Recipes in ... , by W.H.Press et.al., available on-line

Evaluation:

7-scale grade, one (randomly chosen) obligatory exercise and the project. The project should be like a short article with the statement of the problem, description of the way you solve it, and discussion of the results.

Useful links:

[ Linuxbog.dk | GNU scientific library | HTMLhelp | Computer Language Benchmarks ]

Computers:

You can use our servers lifa.phys.au.dk which run RedHat. We also have a dedicated server for numerical methods, genryc, which runs Debian. A lot more software is installed on genryc.

Program examples