TEXT: Lecture notes distributed in class.

Recommended reading: Numerical Computing with MATLAB, Cleve B. Moler, SIAM, Philadelphia, 2004. This book is available for free at http://www.mathworks.com/moler. Software used in class is also available for free at this web site.

INSTRUCTOR:

• Lothar Reichel, office 366 MSB, phone: 330-672-9114, e-mail: reichel@math.kent.edu,
  home page: http://www.math.kent.edu/~reichel
• Office Hours: Tu+Th 2:00-3:30 pm and by appointment.

• Provide an understanding of computational methods, and illustrate their application to the solution of a large variety of problems, including GPS, MP3, text queries, and web search.
• Discuss the errors in computed results, due to errors in the data as well as due to round-off errors introduced during the computations.
• Illustrate the difference in performance of various numerical methods by implementing and comparing them in MATLAB.

• Linear algebra and calculus review
• Introduction to MATLAB/Octave
• Computer arithemtic
• Linear systems of equations
• Orthogonal matrices and the QR factorizationm
• Least-squares problems by QR factorization
• The singular value decomposition and its application to least-squares problems
• Interpolation
• The fast Fourier transform

• Homework will be assigned regularly and collected at the end of each major section. There will be a mid-term exam and a final exam.
• The programming languages MATLAB and GNU Octave will be taught. The performance and properties of the numerical methods discussed will be illustrated using MATLAB. Much of the homework will be to write software in MATLAB or GNU Octave for solving problems discussed in class. All students should get accounts on the Math/CS Network on which MATLAB is available. GNU Octave is a public domain language very similar to MATLAB, and can be used for homework assignments. Instructions on how to install GNU Octave on your PC are available here.

• Homework and numerical experiments contribute 30%, the midterm and final exams contribute 35% each towards the course grade.

• Information can be found at this web site. It is important that everyone registers in time, otherwise late registration fees may have to be paid; click here for further details. Last day to add and be certain not to pay a late fee is August 29(?); last day to drop is September 11, and last day to withdraw is November 6. Plagiarism, i.e., presenting someone else's work as your own is discussed here. This includes finding the answer of a homework problem in a book or in someone else's assignment, and copying it. Plagiarism, of course, is unacceptable.

• will be provided reasonable accommodations to ensure their equal access to course content. Futher information can be found at this web site.

LECTURE NOTES WITH HOMEWORK ASSIGNMENTS:

Basic Concepts and Tools

Computation with Floating-Point Numbers

Linear Systems of Equations and LU Factorization

LU Factorization Applied to GPS Computations

Orthogonal Vectors and Matrices

Least Squares Approximation by QR Factorization

The Singular Value Decomposition

An application to movie rating
A singularly valuable decomposition

The SVD Applied to Signal and Image Deblurring

Blur- and noise-free image

m-file for generating Gaussian blur

m-file for generating motion blur

m-file for generating out-of-focus blur

Searching the Internet with the SVD

Error Bounds for Linear Systems of Equations

Polynomial and Piecewise Polynomial Interpolation

USEFUL LINKS:

• MATLAB is the programming language for this class. A 39-page primer on the basics of MATLAB is available in pdf and in postscript.


• Instead of MATLAB you may run GNU Octave, a public domain alternative; see Lecture 1 for instructions on where to find and how to install GNU Octave.
  


• Here are two links to online MATLAB tutorials:
  • An Introductory Guide to MATLAB
    
  • MATLAB Summary and Tutorial
    


• Software, manuals and glossaries
  • Linear Algebra Glossary
  • The NEOS Software Guide for solving optimization problems remotely over the internet.
  • Decision Tree for Optimization Software (by H. D. Mittelmann and P. Spellucci).
  • GAMS, Guide to Available Mathematical Software.
  • Netlib, a collection of mathematical software, papers, and databases.
  
  
• The importance of reliable software:
  • Two disasters caused by computer arithmetic errors
  August 2009