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Numeriske Metoder. Pensum.
- Integration of functions
- Classical formulas with equally spaced abscissas. Closed and
open formulas.
- Adaptive algorithms with error estimates.
- Gaussian quadratures with optimal abscissas.
- Gauss-Kronrod quadratures.
- Exercise: Adaptive integration with reuse of points.
- Ordinary differential equations
- Single step Runge-Kutta methods.
- Multistep methods. Predictor-Corrector methods.
- Adaptive step-size control.
- Exercise: Runge-Kutta and
Predictor-Corrector with adaptive step-size.
- Linear algebraic equations
- LU decomposition and backsubstitution.
- QR decomposition (modified Gram-Schmidt method) and backsubstitution.
- Exercise: QR decomposition and backsubstitution
- Linear least-squares fit
- Linear least-squares problem and χ² fit with QR-decomposition.
- Covariance matrix.
- Exercise: Linear regression
- Eigenvalues and eigenvectors
-
Jacobi transformation of a real symmetric matrix.
- QR/QL algorithm with explicit shifts.
- Power method. Inverse iteration method.
-
Lanczos tridiagonalization of a real symmetric matrix.
- Exercise: Inverse iteration.
- Interpolation
- Polinomial interpolation. Lagrange interpolating polynomial.
- Rational function interpolation.
- Spline interpolation. Search in an ordered table.
- Derivation and integration of the spline function.
- Exercise: Lagrange interpolating polynomial
and quadratic spline.
- Nonlinear equations.
- Modified Newton's method in multidimensions.
- Obligatory exercise: Modified Newton´s method.
- Minimization of functions.
- Simplex method in multidimensions.
- Obligatory exercise: Simplex method.
- Monte Carlo integration.
- Plain Monte Carlo integration.
- Importance sampling.
- Stratified sampling.
- Quasi-random (Low-discrepancy) sampling.
- Obligatory exercise: Plain Monte Carlo with pseudo- and
quasi-random sampling.
- Simulated annealing methods.
- Metropolis algorithm.
- Simplex method with simulated annealing.
"Copyleft"
© 2004-2006
D.V.Fedorov
(fedorov at phys dot au dot dk)