Undergraduate Course: Numerical Linear Algebra and Applications (MATH10059)
|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 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.
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.
1. Solution of linear systems of equations: condition, direct and iterative methods, consequences of inexact arithmetic, computational cost and exploitation of symmetry, positive definiteness and sparsity
2. Finding a single eigenvalue and eigenvector: condition, iterative methods
3. Applications: superficial general overview and detailed study of particular examples
4. Matlab: commands pertinent to experiments in numerical linear algebra
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Information for Visiting Students
|Pre-requisites||Previous study of linear algebra: matrix (non-)singularity, linear systems of equations, Gaussian elimination, eigenproblem, and matrix transpose, symmetry, positive definiteness and orthogonality
|High Demand Course?
Course Delivery Information
|Academic year 2016/17, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 30%, Examination 70%
||Hours & Minutes
|Main Exam Diet S1 (December)||MATH10059 Numerical Linear Algebra and Applications||2:00|
On completion of this course, the student will be able to:
- Understanding of numerical linear algebra methods for solving linear systems of equations and finding one or more eigenvalues and/or eigenvalues of a matrix.
- Ability to analyse and discuss the computational efficiency of a method, including the influence of sparsity.
- Understanding the concept of conditioning and consequences of using floating-point arithmetic.
- Ability to code simple methods and experiments in Matlab.
- Appreciation of applications which generate subproblems requiring numerical linear algebra techniques.
|Numerical Linear Algebra and Applications by Biswa Nath Datta|
|Graduate Attributes and Skills
||Appreciation that theoretical and textbook techniques may be wholly inadequate in the context of problems of practical interest. Further development of programming skills through the medium of Matlab.
|Additional Class Delivery Information
||18 one-hour lectures
4 two-hour labs
5 one-hour workshops
|Keywords||NLAA,Numerical methods,Linear algebra,Application,Matlab
|Course organiser||Dr Julian Hall
Tel: (0131 6)50 5075
|Course secretary||Mrs Kate Ainsworth
Tel: (0131 6)51 7761
© Copyright 2016 The University of Edinburgh - 3 February 2017 4:42 am