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Matrix Analysis and Algorithms
Systems of Linear Equations (SLE) Least SQuares problems (LSQ)
EigenValue Problems (EVP)
Dr. Bjorn Stinner, Assistant Professor
Mathematics Institute and
Centre for Scientific Computing
University of Warwick
Zeeman Building, Room C2.30
Matrix Analysis and Algorithms Introduction
Objectives
Aim:Understanding the mathematical principles underlying the design and the analysis process
to solve some large scale problems central in numerical linear algebra.
At the end of the module you will familiar with concepts and ideas related to:
• diverse matrix factorisations
– to obtain analytical results,
– as the basis for various algorithms,
• assessing algorithms with respect to computational cost ; efficiency,
• error analysis,
– conditioning of problems,
– stablity of algorithms,
• direct versus iterative methods.
No coding, e.g. module MA4G7 Computational Linear Algebra and Optimization (Term 2).
Dr Bjorn Stinner Term 1, 2010/2011
Matrix Analysis and Algorithms Introduction
Literature
In addition to the lecture notes:
AM Stuart and J Voss, Matrix Analysis and Algorithms, script.
LN Trefethen and D Bau, Numerical Linear Algebra, SIAM 1997.
NJ Higham, Accuracy and Stability of Numerical Algorithms, SIAM 1996.
G Golub and C van Loan, Matrix Computations, 3. ed., Johns Hopkins University Press 1996.
D Kincaid and W Cheney, Numerical Analysis, 3. ed., AMS 2002.
RA Horn and CR Johnson, Matrix Analysis, Cambridge University Press 1985.
JW Demmel, Applied Numerical Linear Algebra, SIAM 1997.
Dr Bjorn Stinner Term 1, 2010/2011
Matrix Analysis and Algorithms Introduction
Relation to Other Modules
MA4G7 Computational Linear Algebra and Optimization (D White)
implementation, coding, software, but also towards optimisation problems.
MA3H0 Numerical Analysis and PDEs (A Dedner)
discretisation of PDEs involves large systems of equations to be solved.
MA3G7 Functional Analysis I (V Gelfreich)
a few ideas notions with respect to norm for the analysis are shared.
MA390 Topics in Mathematical Biology (T House)
problems like pattern formation involve finding eigenvalues of operators.
MA228 Numerical Analysis (X He)
stability and convergence, interpolation, quadrature, ODEs.
Dr Bjorn Stinner Term 1, 2010/2011
Matrix Analysis and Algorithms Introduction
Other Stuff
Assessment: Final exam (100%).
3 question sheets (not relevant for final mark).
Office hours: Wed 11-12, Mon 11-12 (except 11 Oct and 8 Nov)
Web-page: lecture notes, question sheets, etc
http://www.warwick.ac.uk/staff/Bjorn.Stinner/teaching/aut1011.html
Dr Bjorn Stinner Term 1, 2010/2011