MA5233 Computational Mathematics
Mondays 7:00-10:00 pm, S14-06SR
- Lecture 1
Review of linear algebra; orthogonal vectors and matrices, norms,
the singaular value decomposition (SVD), projectors.
- Lecture 2
(27 August): QR factorization; Gram-Schmidt orthogonalization;
Householder triangularization; conditioning and condition numbers;
backward error analysis.
- Lecture 3 (3 September): Gaussian elimination; pivoting; stability of Gaussian elimination; Cholesky factorization.
- Lecture 4 (10 September) : The Arnoldi iteration and GMRES.
- Lecture 5 (17 September) : The conjugate gradient method. Matlab code: CG.m
- Lecture 6 (1 October) : Eigenvalue problems for real symmetric matrices. reduction
to tridiagonal form; Rayleigh quotient and inverse iteration; QR algorithm.
- Lecture 7 (8 October): Introduction to numerical ODE; Consistency, 0-stability, convergence; forward and backward Euler methods; Runge-Kutta method
- Lecture 8 (15 October): Runge-Kutta method; multi-step methods, order condition, root condition
- Lecture 9 (22 October): BDF; finite difference methods for Laplace/Possion equation.
- Lecture 10 (5 November): finite difference methods for diffusion equation; Von Neumann stability analysis.