by KENDALL ATKINSON

Chapters 1-5

- Mathtools.net: a technical computing portal for scientific and engineering needs.
- Some Unix Commands
- Some Emacs Keyboard Commands
- An Overview of Numerical Analysis as discussed by Kendall Atkinson.
- The Definition of Numerical Analysis (pages in reverse order) as discussed by L. N. Trefethen.

- Chapter 1 -
*Preliminaries and a Discussion of Error*- Modelling
- Two disasters due to computer arithmetic error (from Doug Arnold)
- Software bugs (Thomas Huckle)
- Floating-point numbers: pdf.
- IEEE Standard binary number formats
- Floating Point Representation - Michael Overton: pdf
- What Every Computer Scientist Should Know about Floating Point Arithmetic - David Goldberg: pdf
- Computer error example using Log function
- Loss of significance example
- Do loop error example
- The Accuracy Of Floating Point Summation (1993), Nicholas J. Higham.
- Examples of ill-conditioned problems
- Additional references.

- Chapter 2 -
*Rootfinding*- Rootfinding example: graph
- Fortran program bisect.f
- Matlab program bisect.m
- Sample output from bisect.m
- Fortran program newton.f
- Matlab program newton.m
- Newton rootfinding example: table
- Matlab program secant.m
- Secant rootfinding example: table
- Notes on additional
rootfinding methods. (These were originally intended to be included in the
second edition of my text
*An Introduction to Numerical Analysis*). - Test program for zero.f
- Fixed point example for calculating Sqrt(5)
- Fixed point example handouts (in pdf only).
- Finding multiple roots of polynomials has always been a difficult numerical
problem. For a recent excellent algorithm that handles this problem, see the
paper

Zhonggang Zeng, "Computing Multiple Roots of Inexact Polynomials",*Mathematics of Computation***74**(2005), pp. 869-903. - Matlab example: Newton's method for systems
- Graph for Example (2.10.6) of text
- Matlab example: Output
- Notes on optimization.
(These were originally intended to be included in the second edition of my text
*An Introduction to Numerical Analysis*).

- Chapter 3 -
*Interpolation*- Graphs related to interpolation (in pdf only).
- Test program for Fortran program divdif.f
- Fortran program interp.f
- Matlab program divdif.m
- Matlab program interp.m
- Graphs related to polynomial interpolation error (in pdf only).
- Graphs of cubic Hermite basis functions (in pdf only).
- Graphs related to discussion of spline interpolation (in pdf only).
- Spline interpolation example
for
*f(x)=exp(x)*(in pdf only). - Matlab spline routines
- Matlab spline example
- Graph of cubic B-spline
- Interactive Interpolation Example, comparing polynomial and cubic natural spline interpolation. This is due to Tobias von Petersdorff, University of Maryland.
- Notes on multivariate
interpolation (These were originally intended to be included in the second
edition of my text
*An Introduction to Numerical Analysis*).

- Chapter 4 -
*Approximation Theory*- Graphs (in pdf) of Taylor polynomials and errors for log(x)
- The Fortran program for the function SF(x)
- Graph of the function SF(x)
- Graphs of Legendre polynomials of degrees 1,2,3
- Notes on the Remes Algorithm
(These were originally intended to be included in the second edition of my text
*An Introduction to Numerical Analysis*).

- Chapter 5 -
*Numerical Integration & Differentiation*- Graphical illustrations (in pdf only) of the trapezoidal and Simpson rules.
- The Fortran program trapzoid.f
- The Matlab program trapzoid.m
- Fortran program simpson.f
- Matlab program simpson.m
- Examples (in pdf only) of the trapezoidal rule, corrected trapezoidal rule, and Richardson's extrapolation formula.
- Integrate, a Java utility program to do numerical integration examples online.
- Lecture notes for Gaussian quadrature, from C36/M72: pdf
- Examples of Gaussian quadrature
- Fortran program gauss.f
- Matlab program gaussint.m
- Notes on mumerical
differentiation (These were originally intended to be included in the second
edition of my text
*An Introduction to Numerical Analysis*). - Notes on multi-dimensional
integration (These were originally intended to be included in the second
edition of my text
*An Introduction to Numerical Analysis*).

- Matlab
programs to accompany the book
*Elementary Numerical Analysis*. There are also Matlab GUIs for a number of topics, and they are available on the local Engineering and Mathematical Sciences networks. - Sketch A Function. This is a Java utility program to allow online graphing of basic functions.
- Fortran
Programs. These are for the second edition of the book
*Elementary Numerical Analysis*. - C
Language Programs. These are for the second edition of the book
*Elementary Numerical Analysis*. (Let the buyer beware, as I am not a competent C language programmer.)