MATHx6101 Numerical Linear Algebra

Handouts

• Timetable and contact details
• Syllabus
• Assignments: Frequently Asked Questions
• MATLAB
  • Introduction to MATLAB
  • MATLAB Functions
• Basics
  • Background Material ... Solutions to examples.
  • Matrix Multiplication ... Solutions to examples.
  • Matrix Norms ... Solutions to examples.
  • Sensitivity Analysis ... Solutions to examples.
• Matrix factorizations
• Cholesky Factorization ... Solutions to examples.
• QR Factorization ... Solutions to examples.
• LU Factorization ... Solutions to examples.
• LU Factorization Example
• Sparse, Banded Systems and Iterative Solution
• Banded and Sparse Linear Systems
• Iterative Methods ... Solutions to examples.
• CG Method and Preconditioning
• The Kronecker Product
• Linear Least Squares
• Linear Least Squares ... Solutions to examples.
• Eigenvalue Problem
• The Eigenvalue Problem ... Solutions to examples.

MATLAB Worksheets

• Worksheet 1
• Worksheet 2. M-file template: funprobe.m

Further Reading

• Desmond J. Higham and Alan Taylor, The Sleekest Link Algorithm, Mathematics Today, 39(6):192-197, 2003. An article explaining the maths begind Google's PageRank algorithm.
• Nicholas J. Higham, Cholesky Factorization, WIREs Comp. Stat., 1(2):251-254, 2009.
• Nicholas J. Higham, Gaussian Elimination, WIREs Comp. Stat., 3(3):230-238, 2011.

Textbooks

• Course reading list at UoM Library.

The following list comprises a subset of the textbooks on the syllabus that are available electronically (e-books). Note that you must be either on campus or logged in via VPN in order to access SIAM e-books.

• Timothy A. Davis. Direct Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2006. ISBN 0-89871-613-6. xii+217 pp. E-book at SIAM
• James W. Demmel. Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1997. ISBN 0-89871-389-7. xi+419 pp. E-book at SIAM.
• Desmond J. Higham and Nicholas J. Higham. MATLAB Guide, First edition, 2000. Second edition, 2005. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2000. ISBN 0-89871-469-9. E-book at SIAM.
• Nicholas J. Higham. Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, second edition, 2002. ISBN 0-89871-521-0. xxx+680 pp. E-book at SIAM.
• Yousef Saad. Iterative Methods for Sparse Linear System}. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, second edition, 2003. ISBN 0-89871-534-2. xviii+528 pp. E-book at SIAM.
• G. W. Stewart. Matrix Algorithms. Volume I: Basic Decompositions. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001. ISBN 0-89871-503-2. xix+469 pp. E-book at SIAM.
• G. W. Stewart. Matrix Algorithms. Volume II: Eigensystems. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001. ISBN 0-89871-503-2. xix+469 pp. E-book at SIAM.

Links Mentioned in Lectures

• The paper The QR Algorithm: 50 Years Later its Genesis by John Francis and Vera Kublanovskaya and Subsequent Developments, by Gene Golub and Frank Uhlig (2009).
• Cartoon (Daily Mirror, 1952) about Turing and Wilkinson.
• Online Appendix A: Introduction to Matrix Computations, from the book Numerical Methods in Scientific Computing, Volume I, G. Dahlquist and A. Björck, SIAM, 2008.
• The Origins of MATLAB (video), by Cleve Moler.
• The Golden Age of Scientific Computing (video), by Chris Johnson.

Twitter

• @nhigham
• @walkingrandomly - by one of the faculty computer support staff. Contains interesting maths and maths software information.
• @TeXtip - tips on (La)TeX.

Lecturers

• Professor N. J. Higham
• Professor F. Tisseur