Course syllabus
Rationale for a graduate course on
numerical methods (5/16/05)
Data representations
- Slides on integer data representations (5/19/05)
- Slides on floating-point data representations (6/12/05)
Evaluation of functions
- Slides on floating-point computation (5/19/05)
- Slides on numerical integration (5/19/05)
- Slides on Gaussian quadrature (6/29/05)
- Report on the computation of spherical Bessel functions (8/2/88)
Digital filters and aliasing
- Slides on digital filters in numerical computation (6/4/05)
- Slides on aliasing (5/28/05)
Finite-difference methods for ordinary differential equations
- Slides on finite-difference methods (6/14/06)
Systems of linear algebraic equations
- Slides on systems of linear equations (6/9/05)
- Prof. Cantrell's notes on iterative methods for solving systems of linear equations (7/9/06)
Partial differential equations
- Chapter on partial differential equations (8/6/06)
- Example: The paraxial wave equation (PWE)
- Derivation of the PWE (6/10/04)
- Numerical methods for the PWE (6/12/04) (includes finite-difference methods, pseudospectral methods, the Thomas algorithm, and a list of references)
Computer architecture overview,
performance analysis, vectorization and performance enhancement
- Overview of computer architecture (6/15/05)
- Slides on performance analysis (6/12/05)
- Slides on queueing theory (4/30/05)
- Slides on vectorization (4/29/05)
Computer Simulation of Hot Electron Behaviour
in Semiconductors Using Monte Carlo Methods,
by A. D. Boardman (in A. D. Boardman, editor, "Physics Programs",
vol. 4 (New York, Wiley, 1980), pp. 355-410.
Prof. Cantrell's notes
on the method
of conjugate gradients
Parallel Solution of
Pentadiagonal Systems Using Generalized Odd-Even
Elimination, by Creon Levit (in Proceedings of the ACM
Conference on High Performance Numerical Computing, 1989),
pp. 333-336.
Articles on numerical
inversion of the Laplace transform:
- Kenny S. Crump, Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation, Journal of the ACM 23, 89-96 (1976)
- B. S. Garbow et al., Software for an Implementation of Weeks' Method for the Inverse Laplace Transform Problem, ACM Transactions on Mathematical Software 14, 163-170 (1988)
- Errata in the Garbow et al. article