# Syllabus

## Objectives

*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).

## Course Format

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.

## Topics [Applications]

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]

{multiview geometry}

¡@

## References:

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)