Numerical Linear Algebra
Math-6316 and CSE-7366
Spring 2008

• Course description:
  This course will cover the development and analysis of numerical linear algorithms used in the solution of linear equations, eigenvalue problems, and linear least-square problems. It will also cover the Conditioning (related to the problems) and Stability (related to the algorithms) issues. Both dense methods and sparse (iterative) methods will be discussed.
  [ Prerequisites:   Basic knowledge of matrix theory and linear algebra; basic knowledge of computer programming. ]

• Textbooks:
  Lloyd N. Trefethen and David Bau , Numerical Linear Algebra,   SIAM, 1997. ISBN: 0-89871-361-7;
  Alan Laub, Matrix Analysis for Scientists and Engineers,   SIAM, 1997. ISBN-13: 978-0-898715-76-7

• Supplementary textbooks:    
  • Gene Golub and Charles Van Loan , Matrix computations, 3rd Ed., Johns Hopkins University Press, 1996. ISBN: 0-8018-5414-8
  • G. W. Stewart , Matrix algorithms I: Basic decompositions, SIAM, 1998. ISBN: 0-89871-414-1
    G. W. Stewart, Matrix algorithms II: Eigensystems, SIAM, 2001. ISBN: 0-89871-503-2
  • Yousef Saad , Iterative methods for sparse linear systems , SIAM, 2003. ISBN-13: 978-0-898715-34-7.   [1st edition]
  • J. Demmel , Applied numerical linear algebra, SIAM, 1997. ISBN: 0-89871-389-7
  • Henk A. Van der Vorst ,   Iterative Krylov methods for large linear systems, Cambridge University Press, 2003, ISBN: 0521818281.
    Lecture notes on large linear systems and eigenvalue problems
  • D. S. Watkins , Fundamentals of matrix computations, 2nd Ed., Wiley-Interscience, 2002. ISBN: 0-471-21394-2
  • Nicholas J. Higham , Accuracy and Stability of Numerical Algorithms, SIAM, 2002. SBN: 0-89871-521-0.
  • C. Moler, Numerical Computing with MATLAB, SIAM, 2004. ISBN-13: 978-0-898715-60-6 [electronic version]
  • C. D. Meyer , Matrix Analysis and Applied Linear Algebra, SIAM, 2000. [online version]

• Software:    the commercial   Matlab   and/or the open sourceware   Scilab  
• Matlab primer (a bit outdated, but still a good starting point. Do a google search for other online tutorials)
• Scilab tutorial
• Further Readings of interest:
  • NLA at Stanford   [ 13 classic papers in numerical analysis ]
  • NLA at Rice
  • NLA at Berkeley
  • NLA for systems and control
  • Top ten algorithms .   [ the QR algorithm ,   matrix decompositions ,   Krylov methods ]
  • Templates for the Solution of Algebraic Eigenvalue Problems
  • Templates for the Solution of Linear Systems
  • Numerical Computing with IEEE Floating Point Arithmetic
  • Floating Point Arithmetic
    
  • Understanding Search Engines: Mathematical Modeling and Text Retrieval
  • Google's Pagerank and Beyond: The Science of Search Engine Rankings
  • The $25 billion eigenvector: The Linear Algebra Behind Google
    

• Course Policy:
  • Class attendance is required (unless with permission from the instructor)
  • Homework due dates are specified on the webpage
  • Homework counts 45% in total
  • There are two midterms, each counts 15%
  • The final counts 25%