Postgraduate Course: Numerical Linear Algebra and Applications (MATH11196)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Driven by the needs of applications, this course studies reliable and computationally efficient numerical techniques for practical linear algebra problems. As well as traditional theoretical assessment of the techniques studied, Matlab is used to perform practical experiments to complement students' insight into the subject. As a consequence, in addition to the assessment of theoretical understanding and hand calculation via a closed book examination, the course is also assessed via a Matlab class test. |
| Course description |
Linear Algebra is one of the most widely used topics in the mathematical sciences. At level 8 or 9 students are taught standard techniques for basic linear algebra tasks including the solution of linear systems, finding eigenvalues/eigenvectors and orthogonalisation of bases. However, these techniques are usually computationally too intensive to be used for the large matrices encountered in practical applications. NLAA will introduce students to these practical issues and will present, analyse, and apply algorithms for these tasks which are reliable and computationally efficient.
The course includes significant lab work using Matlab and this is assessed in a class test. The theoretical material is assessed in a closed book examination. More advanced material is studied via directed reading and experimentation, and assessed via a written report.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Analyse and discuss the computational efficiency of numerical linear algebra methods for solving linear systems of equations and finding one or more eigenvalues and/or eigenvectors of a matrix, including the influence of sparsity.
- Discuss the implications of problem conditioning and the consequences of using floating-point arithmetic.
- Perform scientific investigation of method by implementing it and performing experiments in Matlab.
- Identify the need for numerical linear algebra techniques to solve subproblems for a range of applications.
- Investigate an unseen topic via directed reading and experimentation, and produce an elementary written scientific report.
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Reading List
Numerical Linear Algebra and Applications, Second Edition", by B. N. Datta, SIAM, ISBN: 978-0-898716-85-6
Numerical Linear Algebra by Lloyd "Nick" Trefethen and David Bau III, SIAM, ISBN: 978-0898713619
Applied numerical linear algebra by James "Jim" Demmel, SIAM, ISBN: 978-0898713893 |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | NLAA,Numerical methods,Linear algebra,applications,Matlab |
Contacts
| Course organiser | Dr Aretha Teckentrup
Tel: (0131 6)50 5776
Email: A.Teckentrup@ed.ac.uk |
Course secretary | Miss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk |
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