MTH3320 - Computational linear algebra

There is a more recent version of this academic item available.

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

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Tiangang Cui

Unit Coordinator(s)

Dr Tiangang Cui

Notes

Additional prerequisite from 2021: You will be required to complete one of MTH2051, MTH3051, ENG1060 or FIT2004. This additional prerequisite won't apply to you if you are enrolled in the Master of Financial Mathematics.

Assessment

1 - Continuous assessment

2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

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.

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Unit course reader, Printing, Stationery)- $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics