Advanced numerical analysis, as the name implies, should be the second course of numerical computing in the curriculum. It is a graduate-level math course.
Frankly, a more suitable name for the course should be "Numerical methods, and their applications in graphics".
I have selected a list of topics that plays important roles in computer graphics. The goal of this course is to get you familiar with the basics, modeling, and solution techniques of these tools.
This course is largely motivated by the courses of Professor Yan-Bin Jia and Professor Michael Erdmann. A great deal of lecture material is borrowed from their online notes. In addition, I intend to cover some aspect of scientific computing using graphics hardware (GPU). It is usually termed as GPGPU (general-purpose graphics processor unit).
The basic (math) material will be covered by the instructor. The selected application will be covered via the student presentation of selected (siggraph) papers. All topics will include either written or programming homework. The use of canned numerical package (e.g., Numerical Recipe) is highly encouraged.
Review of Floating Point Representation (IEEE 754) and Floating Point Computation [watermark embedding]
Symbolic Computation Using Maxima
Review of Numerical Methods; using Canned Software
newton, linear system and condition number, ODE, least square,
Polynomial (evaluation, interpolation, root finding, resultant) [curve intersection]
Singular Value Decomposition [inverse kinematics]
Solution (nonlinear equations, linear equations -- singular value decomposition)
Optimization (linear programming, conjugate gradient)
New Algebraic Construct (plucker coordinate, quaternion) [data registration]
Curve characteristics (parametric curve, frenet frame, algebraic curve)
Numerical Computation Using Graphics Hardware
Linear Programming [melodic similarity, collision detection]
Differential Geometry: Curves [free form deformation 1, 2]
Principal Component Analysis (ref) [OBB Computation]
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C. Cambridge University Press. (Books Online)
Mathematical methods for robotics and vision, Carlo Tomasi (pdf)
GSL, GNU Scientific Library (gsl-for-windows-VC6)