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A list of local and external learning resources relating to numerical
analysis. Please notify me
of any broken link.
Course Related Materials
Outline
of Numerical Analysis Topics: This set of webpages
provide information about numerical analysis topics that students are expected
to learn in numerical analysis course.
Computer codes
from textbook (usename/passwd required)
Comments/ outline of Nonlinear System of equations and Eigenvalue
problems (Math 411 related topics):
(PDF, Postscript)
Math
411 Topics Outline
General
The Definition
of Numerical Analysis:
By L. N. Trefethen, November, 1992 issue of SIAM News (also gzipped
postscript version from author.) Please note that the pages in
the paper appear in reverse order in the file.
Predictions
for Scientific Computing Fifty Years From Now:
By L. N. Trefethen, (also gzipped
postscript version from author)
Numerical Analysis
FAQ
FAQ: Numerical Analysis & Associated Fields Resource Guide.
A text version
in gzip format is also available.
Computational
Science Education Project
CSEP is an electronic book for teaching Computational Science and Engineering.
The intended
audience are students in science and engineering at the advanced undergraduate
level and higher.
Tutorials for freely available networking and visualization software
are included and have attracted
a range of users, including high-school students and people from the
commercial sector.
Unsolved Mathematics
Problems:
For the curious minds. From Mathsoft (maker of Mathcad).
References not on the web
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Seven Deadly Sins of Numerical Computation, B. J. McCartin, American
Math. Monthly, vol 105, num. 10, Dec 1988, pp 929--941. |
[abstract: Nowhere is the old adage "a little knowledge is a dangerous
thing" more apropos than in numerical computation. With minimal expertise
and a powerful computer, the novice may now boldly attempt to simulate
the physical world in which we are all embedded. However, this is essentially
an invitation to 'shoot oneself in the foot' unless certain subtle pitfalls
inherent in passing from continuum models of reality to the discrete domain
of the digital computer are studiously avoided. We discuss seven of the
most egregious such transgressions.]
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Numerical Methods that
Works, Forman Acton, reprinted by MAA, 1990, originally published in
1970. |
Software Information and Sources
Netlib Repository
Netlib is a collection of mathematical software, papers, and databases
NIST Guide to Available Mathematical
Software
A cross-index and virtual repository of mathematical and statistical
software components of use in computational science and engineering. National
Institute of Standards and Technology
Freely
available linear algebra software:
This is a good place to start your search of high quality linear algebra
software. Maintained by Jack Dongarra.
Numerical Recipes
People have been arguing for a while about the routines in Numerical Recipes.
My view is that if you are performing preliminary
studies or solving some toy problems
and do not care much about carrying all the overhead that usually accompany
quality software, by all means use the routines in the book. Likewise,
if you only want to have a very superficial understanding of the algorithms,
the book does give an excellent overview of the basic ideas behind the
numerical methods. The content of the book is accessible but
the source code is a separate commercial product.
Numerical Recipes by Press, Teukolsky, Vetterling,
and Flannery
For those people who think Numerical Recipes is the best there is,
have a look at the following objections. (Rebuttal of these objections
may be found in the official Numerical Recipes website.
Why not Numerical Recipes?
Why not
Numerical Recipes in C?
Papers
Google Scholar
NEC CiteSeer
An excellent scientific literature digital library.
Los Alamos e-Print archive
This is an archive of preprints or published papers in physics, mathematics
and computer science: includes the Computing
Research Repository (CoRR).
Java
Javanumerics:
This is a good starting point for information on numerical computing
in Java.
Mathematical Software Tutorials
Matlab
The Math department has only a limited number of licenses. Accessible
from computers on Labnet and in the Math Lab in 159 TMCB.
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Kermit's Primer:
This popular tutorial has now been published by CRC. Earlier postscript
versions may still be found on the net. (Try searching on e.g. www.altavista
using "matlab primer") |
Maple
This software is available campus wide.
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Maple:
An Introduction: Useful summary of maple by Dominik Gruntz, et
al (Institute for Scientific Computation, ETH Zurich) |
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Maple
Lab Manual: A useful guide to learning maple, by
W. Farr (Worcester Polytechnic Institute ) |
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Maple Tutorial:
Info on using worksheets, printing, etc. - from University of Texas at
Austin. Some general material are useful. |
Mathematica
The Math department has only a limited number of licenses. Accessible
from computers in the Math Lab in TMCB.
Selected Topics in Numerical Analysis
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Nonlinear Equations |
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Bisection method |
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Newton's method |
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Secant method |
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Floating Point Systems |
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Direct Methods for System of Linear Equations |
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Iterative Methods for System of Linear Equations |
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General Theory |
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Jacobi Iteration |
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Gauss Seidel Iteration |
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SOR Iteration |
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Least Squares Problems |
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Continuous Least Squares |
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Orthogonal Polynomials |
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Three-term recurrence relation |
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Polynomial Interpolation |
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Lagrange Interpolation |
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Divided difference form |
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Hermit Interpolation |
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Cubic Spline |
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Numerical Differentiation |
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Richardson's extrapolation |
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Numerical Integration |
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Newton-Cotes |
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Adaptive Quadrature |
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Romberg Integration |
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Gauss Quadrature |
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Nonlinear
System of Equations |
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Ordinary Differential Equations |
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Runge Kutta Methods |
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Multistep Methods |
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Stability |
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Boundary Value Problems |
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Approximation Theory |
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Trigonometric Polynomials |
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Fast Fourier Transform |
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Pade Approximation |
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Finite Difference Method |
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Derivation |
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Stability |
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Lax Equivalence Theorem |
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Finite Element Method |
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Finite Volume Method |
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Boundary Element Method |
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Krylov Subspace Methods |
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Steepest Descent |
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Conjugate gradient |
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GMRES |
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Singular Perturbation Problems |
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Homogenization |
| Bifurcation |
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Mathematical Programming |
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