Science Mathematics and Statistics

Numerical Linear Algebra (MATH5371)

Overview

MATH5371 is a Honours and Postgraduate Coursework Mathematics course.

Units of credit: 6

Prerequisites: N/A

Exclusion courses: MATH3371 - jointly taught 

Cycle of offering: Term 1 2022

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. This will be provided closer to the start of term. 

 The Online Handbook entry contains information about the course timetable. 

If you are currently enrolled in MATH5371, you can log into UNSW Moodle for this course.

Course aims

  • Understand algorithms for simple operations in linear algebra, and how their computational costs scale with problem sizes.
  • Present the use of key matrix factorisations (LU, QR, SVD) for solving standard problems in linear algebra.
  • Show how to recognise and exploit matrix structures (symmetry, band width, sparsity) for improving the efficiency of key algorithms.
  • Explain the role and basic features of selected iterative methods (QR iteration, Jacobi, Richardson, conjugate gradient).
  • Introduce some applications illustrating the wide range of applications of numerical linear algebra (data fitting, low-rank approximation, principal component analysis, image compression, machine learning).

Course descriptions

Algorithms from numerical linear algebra are ubiquitous in scientific and statistical software. The theoretical component of the course aims to impart an understanding of how these algorithms work as well as an appreciation of their potential limitations. Familiar pencil-and-paper methods suitable for solving small problems by hand calculation must typically be modified or replaced by different approaches when faced with large problems whose solution is feasible only with the help of a computer.

To illustrate the applications of numerical linear algebra, a variety of examples from statistics, data science and applied mathematics are described. The course includes a substantial computing component providing practical experience with widely used software libraries.