| Week |
Sunday Lecture |
Thursday Lecture |
| 1 |
18/10/2009
Overview of the syllabus, linear interpolation, polynomial interpolation - the straight forward approach, Lagrange polynomial, the Neville method (139KB) |
22/10/2009
How good is the polynomial interpolation? Tradeoff between accuracy and complexity, Splines (117KB) |
| 2 |
25/10/2009
Clarifications for the last lesson, regular grids intepolation (124KB) |
29/10/2009
Convolution and interpolation, interpolating in higher dimensions (97KB) |
| 3 |
01/11/2009
Integration - bounding the error using simplistic analysis and using taylor series. |
05/11/2009
How good is the Simpson method? Integration in higher dimensions - Monte Carlo integration (107KB) |
| 4 |
08/11/2009
Monte Carlo Integration - sampling distributions, Non-linear equations - bisection method, Newton-Raphson (115KB) |
12/11/2009
Some additions to Monte Carlo Integration and error assesment in Newton-Raphson, Linear equations - Gaussian elimination, LU factorization (84KB) |
| 5 |
15/11/2009
Existence of LU decomposition, Cholesky decomposition (71KB) |
no class |
| 6 |
22/11/2009
Iterative methods for solving linear systems, matrix operatory norm, Jacobi's method (93KB) |
26/11/2009
Gauss-Seidel method, steepest descent method (88KB) |
| 7 |
29/11/2009
Steepest descent - error and convergence analysis (82KB) |
03/12/2009
Conjugate gradients - intuition and details (78KB) |
| 8 |
06/12/2009
Making CG a bit more efficient, summary of linear solvers (77KB) |
10/12/2009
Pre-conditioning (86KB) |
| 9 |
Happy Hanukkah! |
class cancelled |
| 10 |
20/12/2009
Preconditioning, PCG - transformed and untransformed (83KB) |
24/12/2009
CG and PCG, example: Poisson equation and the Diffusion equation (68KB) |
| 11 |
27/12/2009
Eigenvector decomposition: the power method (74KB) |
31/12/2009
The power method, finding small eigenvalues, inverse power method (62KB) |
| 12 |
03/01/2010
Jacobi Iteration (74KB) |
07/01/2010
Arnoldi and Lanczos (52KB) |
| 13 |
10/01/2010
QR decomposition, optimization - bracketing, downhill simplex (90KB) |
14/01/2010
Bracketing explained, line minimization, minimization using derivatives, random methods (77KB) |
| 14 |
no class |
21/01/2010
Differential equations (182KB) |
| |
All Lectures (2.08MB) |