Math 523
Numerical Analysis I:
Algorithmic Introduction to Scientific Computation
A basic recipe course on useful methods used in modern
scientific computation, emphasizing on the algorithms and their
implementations.
- Matrix computation and linear system
- Matrix decomposition, LU and QR
- Basic iterative methods
- Conjugate-gradient
- Power methods and QR algorithms for eigen-problems
- Nonlinear equations and optimization
- Newton's methods
- Quasi-Newton methods
- Line search methods
- Data and signal analysis
- Interpolation
- Splines
- Least square fitting
- Fourier and wavelet transforms
- Random numbers, Monte Carlo sampling
- Numerical Quadrature
- Simple integration rules
- Gaussian quadratures
- Monte Carlo integration
- Differential equations
- Euler method, Verlet scheme, Runge-Kutta
- Stiff solvers
- Finite difference marching method for time depenent equations
- Finite element for Variational problems