MTH4320 Computational linear algebra
Faculty of Science
MTH4320 Computational linear algebra is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2026 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2026
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2026 handbook entry. See the 2027 entry.
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Requisites
Before MTH4320
No prerequisites or corequisites besides the enrolment rules below.
After MTH4320
No unit lists MTH4320 as a prerequisite in the 2026 handbook.
Enrolment rules
Prohibition: MTH3320
You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
Overview
The overall aim of this unit is to study the numerical methods for matrix computations that lie at the core of a wide variety of large-scale computations and innovations in the sciences, engineering, technology and data science. You will receive an introduction to the mathematical theory of numerical methods for linear algebra (with derivations of the methods and some proofs). This will broadly include methods for solving linear systems of equations, least-squares problems, eigenvalue problems, and other matrix decompositions. Special attention will be paid to conditioning and stability, dense versus sparse problems, and direct versus iterative solution techniques. You will learn to implement the computational methods efficiently, and will learn how to thoroughly test their implementations for accuracy and performance. You will work on realistic matrix models for applications in a variety of fields. Applications may include, for example: computation of electrostatic potentials and heat conduction problems; eigenvalue problems for electronic structure calculation; ranking algorithms for webpages; algorithms for movie recommendation, classification of handwritten digits, and document clustering; and principal component analysis in data science.
Offerings in 2026
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Critically evaluate and synthesise the mathematical theory behind a selection of important numerical methods for linear algebra, including the derivation of the methods and the analysis of their properties.
- 2
Analyse and apply advanced concepts of conditioning, stability, accuracy, convergence, convergence speed, and computational cost, demonstrating a thorough understanding of these notions in complex scenarios.
- 3
Exhibit mastery in the most important linear algebra algorithms for solving linear systems, least-squares problems, eigenvalue decompositions, and other matrix decompositions, applying these methods to complex problems in science, engineering, technology, and big data analytics.
- 4
Design, implement, and critically evaluate advanced computational linear algebra methods, demonstrating the correctness and efficiency of the implementations through systematic and rigorous computational tests.
- 5
Communicate complex theoretical and applied computational linear algebra problems with clarity and precision, both in written and oral forms, suitable for academic and professional audiences
Workload and teaching
- Seminars36 hours
- Applied sessions22 hours
- Teaching approachActive learning
Three 1-hour seminars;
One 2-hour applied class (in weeks 2-12) and
7 hours of independent study per week
Learning resources
Resources
Ascher UM, Greif C. A First Course in Numerical Methods. Society for Industrial and Applied Mathematics; 2011. http://epubs.siam.org.ezproxy.lib.monash.edu.au/doi/book/10.1137/9780898719987 <http://epubs.siam.org.ezproxy.lib.monash.edu.au/doi/book/10.1137/9780898719987>
Bjorck A. Numerical methods in matrix computations. Springer; 2015. https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/978-3-319-05089-8 <https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/978-3-319-05089-8>
Demmel JW. Applied numerical linear algebra. Society for Industrial and Applied Mathematics; 1997. http://epubs.siam.org.ezproxy.lib.monash.edu.au/doi/book/10.1137/1.9781611971446 <http://epubs.siam.org.ezproxy.lib.monash.edu.au/doi/book/10.1137/1.9781611971446>
Gander W, Gander MJ, Kwok F. Scientific computing-An introduction using Maple and MATLAB. Springer; 2014. https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/978-3-319-04325-8 <https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/978-3-319-04325-8>
Linge S, Langtangen HP. Programming for Computations-MATLAB/Octave: A Gentle Introduction to Numerical Simulations with MATLAB/Octave. Springer; 2016. https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/978-3-319-32452-4 <https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/978-3-319-32452-4>
Quarteroni A, Sacco R, Saleri F. Numerical mathematics. Springer; 2010. https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/b98885 <https://link-springer-com.ezproxy.lib.monash.edu.au/book/10.1007/b98885>
Saad Y. Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics; 2003. http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf <http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf>
Saad Y. Numerical Methods for Large Eigenvalue Problems: Revised Edition. Society for Industrial and Applied Mathematics; 2001. http://www-users.cs.umn.edu/~saad/eig_book_2ndEd.pdf <http://www-users.cs.umn.edu/~saad/eig_book_2ndEd.pdf>
Trefethen LN and Bau D. Numerical linear algebra. Society for Industrial and Applied Mathematics; 1997. On overnight reserve in library.
Contacts
- Unit Coordinators
- Dr Mark Flegg
- Chief Examiners
- Dr Mark Flegg
Common questions
What are the prerequisites for MTH4320?
MTH4320 has no prerequisites, but enrolment rules apply.
When is MTH4320 offered?
In 2026, MTH4320 runs in Semester 1 at Clayton.
Does MTH4320 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.