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Programme & Unit Catalogues

MA30051: Numerical linear algebra

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 1
Assessment: CW 25%, EX 75%
Supplementary Assessment: MA30051 Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA20216 and take MA20218 and take MA20222
Description: Aims:
To teach an understanding of iterative methods for standard problems of linear algebra.

Learning Outcomes:
Students should know a range of modern iterative methods for solving linear systems and for solving the algebraic eigenvalue problem. They should be able to anayse their algorithms and should have an understanding of relevant practical issues.

Content:
Topics will be chosen from the following: The algebraic eigenvalue problem: Gerschgorin's theorems. The power method and its extensions. Backward Error Analysis (Bauer-Fike). The (Givens) QR factorization and the QR method for symmetric tridiagonal matrices. (Statement of convergence only). The Lanczos Procedure for reduction of a real symmetric matrix to tridiagonal form. Orthogonality properties of Lanczos iterates.
Iterative Methods for Linear Systems: Convergence of stationary iteration methods. Special cases of symmetric positive definite and diagonally dominant matrices. Variational principles for linear systems with real symmetric matrices. The conjugate gradient method. Krylov subspaces. Convergence. Connection with the Lanczos method.
Iterative Methods for Nonlinear Systems: Newton's Method. Convergence in 1D. Statement of algorithm for systems.
Programme availability:

MA30051 is Optional on the following programmes:

Department of Computer Science
• USCM-AFB01 : BSc Computing (Full-time) - Year 3
• USCM-AKB01 : BSc Computing (Full-time with Thick Sandwich Placement) - Year 4
• USCM-AFB20 : BSc (hons) Computer Science and Mathematics (Full-time) - Year 3
• USCM-AKB20 : BSc (hons) Computer Science and Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USCM-AAB20 : BSc (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USCM-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 3
• USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• TSMA-AFM09 : MSc Mathematical Sciences (Full-time)
• TSMA-APM09 : MSc Mathematical Sciences (Part-time)
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time)
• TSMA-AWM14 : MSc Modern Applications of Mathematics (Full-time incorporating placement)
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time)

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.