TEACHING NUMERICAL ANALYSIS USING
AN INTRODUCTION TO NUMERICAL ANALYSIS
by KENDALL ATKINSON

E_mail: Kendall-Atkinson@uiowa.edu

GENERAL INFORMATION

• 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.

Miscellaneous notes

• 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).

Programs:

• 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.)

Atkinson's home page