MTH3320 - Computational linear algebra

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 Mark Flegg

Unit Coordinator(s)

Dr Mark Flegg

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.

Learning outcomes

On successful completion of this unit, you should be able to:

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.

Explain and apply notions of conditioning, stability, accuracy, convergence, convergence speed and computational cost.

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.

Implement advanced computational linear algebra methods, and demonstrate the correctness and efficiency of the implementations in systematic computational tests.

Demonstrate advanced skills in the written and oral presentation of theoretical and applied computational linear algebra problems.

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

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