MTH3320 Computational linear algebra
Faculty of Science
MTH3320 Computational linear algebra is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2021 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2021
- Semester 1
- Clayton
- Assessment
- Exam 60%
- and 1 other task
This is the 2021 handbook entry. See the 2027 entry.
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Requisites
Before MTH3320
No prerequisites or corequisites besides the enrolment rules below.
After MTH3320
No unit lists MTH3320 as a prerequisite in the 2021 handbook.
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 2021
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentOtherThreshold hurdle40%
- Examination (3 hours and 10 minutes)ExamThreshold hurdle60%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Explain 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
Explain and apply notions of conditioning, stability, accuracy, convergence, convergence speed and computational cost.
- 3
Demonstrate proficiency in the main linear algebra algorithms for solving linear systems, least-squares problems, eigenvalue decompositions, and other matrix decompositions, and apply them to problems in science, engineering, technology and big data analytics.
- 4
Implement advanced computational linear algebra methods, and demonstrate the correctness and efficiency of the implementations in systematic computational tests.
- 5
Demonstrate advanced skills in the written and oral presentation of theoretical and applied computational linear algebra problems.
Workload and teaching
- Lectures36 hours
- Applied sessions16.5 hours
- Three 1-hour lectures and
- One 1.5-hour applied class per week (in weeks 2-12)
Learning resources
Required 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.
Where it fits
MTH3320 is part of 7 areas of study in the 2021 handbook.
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- APPLMTH07Applied mathematics elective unitsApplied mathematicsNo reviews yet
- FININMAT03Financial and insurance mathematics elective unitsFinancial and insurance mathematicsNo reviews yet
- MTHSTAT07Mathematical statistics elective unitsMathematical statisticsNo reviews yet
- MATHS09Mathematics elective unitsMathematicsNo reviews yet
- MATHS11Mathematics elective unitsMathematicsNo reviews yet
- MATPURE07Pure mathematics elective unitsPure mathematicsNo reviews yet
Contacts
- Unit Coordinators
- Dr Tiangang Cui
- Chief Examiners
- Dr Tiangang Cui
Common questions
What are the prerequisites for MTH3320?
MTH3320 has no prerequisites, but enrolment rules apply.
When is MTH3320 offered?
In 2021, MTH3320 runs in Semester 1 at Clayton.
Does MTH3320 have an exam?
Yes. The exam is worth 60% of the final mark, alongside 1 other task.
Which majors and minors include MTH3320?
MTH3320 is part of Applied mathematics; Financial and insurance mathematics; Mathematical statistics; Mathematics; and Pure mathematics.