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MA30365: Numerical linear algebra

[Page last updated: 22 May 2025]

Academic Year: 2025/26
Owning Department/School: Department of Mathematical Sciences
Credits: 12 [equivalent to 24 CATS credits]
Notional Study Hours: 240
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: CWRI 25%, EXCB 75%
Assessment Detail:
  • MA32065 Examination (EXCB 75%)
  • MA32065 Mini project (CWRI 25%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA22037 OR take MA20222
In taking this module you cannot take MA30051
Learning Outcomes: By the end of the unit, you will be able to:
  • use numerical methods for solving linear systems and algebraic eigenvalue problems with a computer,
  • analyse the behaviour of these methods with rigorous mathematics,
  • and appraise relevant practical issues in applying these techniques to solve real-world problems.



Synopsis: You will study modern iterative methods for solving linear systems and for solving the algebraic eigenvalue problems, including the analysis of algorithms and practical issues in solving problems in science and engineering.

Content: Topics will be chosen from the following: Linear matrix eigenvalue problem: The Schur form. The power method and its extensions. Subspace methods. Error analysis and convergence theory. Perturbation theory. Givens/Householder QR factorization and the QR method. The Lanczos method and extensions. Krylov subspace methods. The Jacobi algorithm. The Divide and Conquer method. Extensions to generalised and nonlinear eigenvalue problems. Special matrix classes and applications. The Singular Value Decomposition and applications. Iterative methods for linear systems: Convergence of stationary iteration methods. Descent methods and the conjugate gradient method and extensions. Krylov subspace methods and preconditioners. Relationship between Lanczos and conjugate gradient method. Error bounds and perturbation theory. Convergence and extensions. Special matrix classes and applications.

Course availability:

MA30365 is Optional on the following courses:

Department of Mathematical Sciences
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
  • 好色tv and units are subject to change 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.
  • Find out more about these and other important University terms and conditions here.