CS7ET01 Numerical Methods and Advanced Mathematical Modelling
Year 20072008
Lecturer: Rozenn Dahyot
Interesting Online references:
 Linear Algebra, book by Jim Hefferon.
 Numerical recipes in C William H. Press, Saul A. Teukolsky, William Vetterling and Brian P. Flannery, 1992
 The Matrix Cookbook, K. Brandt Petersen & M. Syskind Pedersen, Sept. 2007.
 Mathematical Optimization in Graphics and Vision, P.C.Pinto Carvalho and L. Velho, SIGGRAPH 2003.
 Practical LeastSquares for Computer Graphics, F. Pighin & J. P. Lewis, Siggraph 2007.
 Numerical Computing with MATLAB, by Cleve Moler.
Other references:
 Applied Partial Differential Equations, J. David Logan, Springer 1991.
 Digital Signal and Image Processing using Matlab, G. Blanchet and M. Chaubit, ISTE 2001.
 Introduction to Numerical Ordinary and Partial Differential Equations using matlab, A. Staneoyevitch, Wiley 2005.
Software
 Matlab is used and is available in the lab.
 Octave, a free alternative to matlab, almost fully compatible with Matlab.
Assignments:
 1st term assignment. It is to hand in at the end of Michaelmas term (7/12/2007) at my office.
 2nd term assigngment. It is to hand in at the end of Hilary term (5/03/2008) in class or in my office.
 Marks
Lecture notes:
 Introduction and revisions of Linear Algebra, 10/10/2007
 Least Squares, 11 Oct. 2007.

Principal Component Analysis 17 Oct. 2007.
 Example of least squares, matlab file
 Example of PCA, matlab file
 Example of application of PCA, powerpoint file.
 Tutorial, 18 October 2007.
 lecture on optimization, 24 October 2007.

lecture on ODE, 31 October 2007.
 Applied Partial Differential Equations, J. David Logan, Springer, 1998 (Appendix A).
 solution to exercises on ODE.

lecture on ODE (finding numerical solutions), 1 Nov. 2007.
 Games and Physics: Design Issues by C. Low at HP. This is an easy reading illustrating the use of ODE with numerical methods (e.g. section 5).

lecture on ODE (2nd order) with Laplace Transform, 7 Nov. 2007.
 exercise, 8 Nov. 2007

lecture on PDE, 14 Nov. 2007.

Extras:
 solution to the diffusion equation with xls file, 15 Nov. 2007.
 Image Processing : a DSP application with slides.

lecture on Method of Weighted Residuals, 21 and 22 Nov. 2007.
 Some answers to exercises, 21 and 22 Nov. 2007.

Notes on Dirac function, and Vector space, 29 Nov. 2007.
 Exercise Galerkin Formulation of Poisson's equation, 2829 Nov. 2007.
 Fourier transform, 5 Dec. 2007.

Discrete Fourier Transform, 6 Dec. 2007.
 Answers to exercises on DFT, 6 Dec. 2007.
 p.d.f., nonparametric estimate of p.d.f., parameters, moments and statistics, January 10th, 2008.
 parametric estimate of p.d.f., marginals, joint p.d.fs, January 16th, 2008.
 Classification, transformation of random variable, January 17th, 2008.
 Hough and Radon transforms, January 23rd, 2008.
 Kalman Filter, January 24th, 2008.
 The inversion method, January 30th, 2008.
 Numerical integration, January 31st, 2008.
 Sampling theorem, February 6th, 2008.

Notes on wavelets, February 14th, 2008.
 wavelets for computer graphics, E. J. Stollnitz, T. D. DeRose and D. H. Salesin, 1995
 Texture synthesis, sigmedia group.
 sound texture synthesis here and here, Deirdre O'Regan
 Link in between least square estimation and normality assumption on the residuals, 20 February 2008

Differences in between PCA and least squares
 example of matlab code, 21 Feb. 2008
 Reminder Newton Raphson, 21 Feb. 2008
 gradient methods, 27 Feb. 2008
 Correction Assignments 1 & 2, 56 March 2008
Articles:

Illustration of Least Squares in Computer graphics:
 LeastSquares Meshes, O. Sorkine and D. CohenOr, proceeding of shape Modeling International, pp. 191199, 2004