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MA50178: Numerical linear algebra

Follow this link for further information on academic years Academic Year: 2014/5
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment Summary: CW 40%, EX 60%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 40%)
  • Examination (EX 60%)
Further information on supplementary assessment Supplementary Assessment: MA50178 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites:
Further information on descriptions Description: Aims & Learning Objectives:
To teach an understanding of iterative methods for standard problems of linear algebra. 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, for large scale problems. They should be able to demonstrate an in-depth understanding of the subject.

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.
Further information on programme availabilityProgramme availability:

MA50178 is Compulsory on the following programmes:

Department of Mathematical Sciences

MA50178 is Optional on the following programmes:

Department of Mathematical Sciences
* This unit catalogue is applicable for the 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* 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.