(Created 2009-08-11.)
 NUMERICAL LINEAR ALGEBRA FMNN01

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English. Optional for: E4, F4, Pi4, Pi4bs. Course coordinator: Johan Helsing, helsing@maths.lth.se, Numerisk analys. Recommended prerequisits: Basic course in numerical analysis (FMN011, FMN041, FMN050 or FMN081), FMA036 Linear Analysis. The course might be cancelled if the numer of applicants is less than 10. Assessment: Graded, weekly homework. Home page: http://www.maths.lth.se/na/courses/NUM115.

Aim
The course provides theoretical understanding of some very useful algorithms. The course also provides hands-on experience of implementing these algorithms as computer code and of using them to solve applied problems. Upon completion of the course the student shall have substantially better and more useful knowledge of numerical linear algebra than students who only have completetd a regular basic course in scientific computing. The course shall also stimulate to a continued independent study.

Knowledge and understanding
For a passing grade the student must

have demonstrated substantially better and more useful knowledge of numerical linear algebra than students who only have completetd a regular basic course in scientific computing.

Skills and abilities
For a passing grade the student must

have obtained hands-on experience of implementing algorithms as computer code and of using them to solve applied problems.

Judgement and approach
For a passing grade the student must

write a locically well-structured report in adequate terminology on weekly homework dealing with the construction and application of advanced algorithms in linear algebra.

Contents
The course is a follow-up to the basic course Linear Algebra. We teach how to solve practical problems using modern numerical methods and computers. Central concepts are convergence, stability, and complexity (how accurate the answer will be and how rapidly it is computed). Other tools include matrix factorization and orthogonalization. Algorithms covered can, among other things, be used to solve very large systems of linear equations that arise when discretizing partial differential equations, and to compute eigenvalues.

Literature
Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, SIAM, Philadelphia, ISBN 0-89871-361-7