NUMERICAL ANALYSIS : M170/C170

Syllabus

Text Book: An Introduction to Numerical Analysis, second edition, by K. Atkinson. Available from IMU Bookstore or Iowa Book and Supply. For other sources for purchasing books, often at a lower cost, click here. In some cases, you can get a book at a significantly lower price than locally, provided you are willing to wait for it to be mailed to you.

E_mail: Kendall-Atkinson@uiowa.edu

Weekly Schedule

GENERAL INFORMATION

Matlab Primer (for an earlier version of Matlab)
A Matlab tutorial from the University of New Hampshire
MATLAB Online Reference Documentation provides direct hypertext links to specific MATLAB function descriptions (from the Math Dept, University of Florida).
Matlab Help Desk (including manuals).
Mathworks, Inc., producers of Matlab.
Mathtools.net: a technical computing portal for scientific and engineering needs.
Some Unix Commands
Some Emacs Keyboard Commands
Fortran Programs From Elementary NA Textbook
C Language Versions of Programs From Elementary NA Textbook (Let the buyer beware, as I am not a competent C language programmer.)
Mathematics/Statistics Educational Laboratory (MSEL)
The Definition of Numerical Analysis as discussed by L. N. Trefethen.
Maxims about numerical mathematics, science, computers, and life on earth as discussed by L. N. Trefethen.
An Overview of Numerical Analysis by Kendall Atkinson.

E_mail: Kendall-Atkinson@uiowa.edu

CLASS ACCOUNT: The class account is at
/group/class/c170
Merely use the cd command to move to that subdirectory.

Assignments

"The purpose of computing is insight, not numbers." - Richard Hamming

I include this quote to indicate that I want something more than pages of output when assigning problems requiring computing. Comment on your output and on the process by which it was produced. Discuss the numerical method used in light of the output you produce. Using carefully chosen graphs is often a good means of giving additional insight.

Miscellaneous notes

Chapter 1 - Preliminaries and a Discussion of Error
- Modelling
- Disasters due to computer arithmetic error (from Doug Arnold, PSU)
- Software bugs (Thomas Huckle)
- Floating-point numbers: ps or pdf.
- IEEE Standard binary number formats
- The Intel Floating-Point Unit
- Floating Point Representation - Michael Overton: ps or pdf
- What Every Computer Scientist Should Know about Floating Point Arithmetic - David Goldberg: ps or pdf
- Bibliography of material on floating-point arithmetic
- IBM page on decimal floating-point arithmetic
- 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).
- 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: ps or 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).

Sketch A Function

CONDENSED PRINTING

To condense and print two postscript pages on a single regular sized sheet of paper, use the command
psnup -pletter -nup 2 input_file.ps output_file.ps
This produces a new postscript file, and it can then be printed using your usual print command for such files.

Atkinson's home page