Undergraduate Course: Numerical Linear Algebra (MATH10098)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 3 Undergraduate)
||Availability||Available to all students
|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 algorithms studied, an advanced programming language is used to perform practical experiments to complement students insight into the subject.
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. This course 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 an advanced programming language. The course studies three main topics: the solution of linear systems of equations, the solution of least squares problems and finding the eigenvectors and/or eigenvalues of a matrix.
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of any pre-requisite course listed above before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 18,
Seminar/Tutorial Hours 5,
Supervised Practical/Workshop/Studio Hours 12,
Summative Assessment Hours 1.5,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 50%, Examination 50%
||Hours & Minutes
|Main Exam Diet S1 (December)||2:00|
On completion of this course, the student will be able to:
- Use the algorithms presented in the course to solve linear systems of equations, solve least squares problems and find eigenvalues and eigenvectors of a matrix, and choose an appropriate method for a given problem.
- Develop methods to solve numerical linear algebra problems using the tools presented in the course.
- Analyse the computational cost of an algorithm and discuss its computational efficiency.
- Discuss the accuracy of computed solutions in reference to matrix conditioning, floating point arithmetic and convergence of iterative methods.
- Perform scientific investigation of an algorithm by implementing it and performing experiments in Python.
|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
|Graduate Attributes and Skills
|Course organiser||Dr Aretha Teckentrup
Tel: (0131 6)50 5776
|Course secretary||Miss Greta Mazelyte