The module descriptors for this programme can be found below.
Modules shown are for the current academic year and are subject to change depending on your year of entry.
Please note that the curriculum of this programme is currently being reviewed as part of a College-wide process to introduce a standardised modular structure. As a result, the content and assessment structures of this course may change for your year of entry. We therefore recommend that you check this course page before finalising your application and after submitting it as we will aim to update this page as soon as any changes are ratified by the College.
Find out more about the limited circumstances in which we may need to make changes to or in relation to our courses, the type of changes we may make and how we will tell you about changes we have made.
Computational Linear Algebra
Module aims
The module provides the student with both a theoretical and practical understanding of the standard algorithms for solving simultaneous linear equations (Ax=b), as well as of the challenges involved. It also provides the student with both a theoretical and practical understanding of the standard algorithms for efficient solution of eigenvalue problem and singular value decomposition and their applications in data compression and Principal Component Analysis (PCA).
Learning outcomes
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At completion of the course, students should be able to:• Use state-of-the-art iterative methods, including sensitivity analysis of eigenvalues and eigenvectors to adjust response of a system.• Regularise and apply SVD to ill-posed problems• Utilize PCA and its application in data reduction and image processing.• Use Chebyshev acceleration, conjugate gradient method and GMRES as optimisation algorithms.• Define and implement the classical iterative algorithms• Implement Gaussian elimination with pivoting, LU and Cholesky factorisations as a numerical algorithm
Module syllabus
1 Introduction to the course; review of vector spaces, vector and matrix norms; floating point numbers and arithmetic.
2 Backward stability, accuracy of approximate solutions to linear systems, condition number; introduction to direct methods for linear systems; forward & backward substitution for triangular systems.
Pre-requisites
Basic linear algebra (basis vectors, eigenvectors).
Teaching methods
Assessments
This module presents opportunities for both formative and summative assessment. You will be formatively assessed through progress tests and tutorial sessions. You will have additional opportunities to self-assess your learning via tutorial problem sheets. You will be summatively assessed through a 2-hour written closed-book examination.