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.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

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

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.