Academic Year: 
2014/5 
Owning Department/School: 
Department of Mathematical Sciences 
Credits: 
6 
Level: 
Honours (FHEQ level 6) 
Period: 
Semester 1

Assessment Summary: 
CW 25%, EX 75% 
Assessment Detail: 
 Coursework (CW 25%)
 Examination (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 (BauerFike). 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
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
 USCMAAB14 : BSc(Hons) Computer Science with Mathematics with Study year abroad (Year 4)
 USCMAKB14 : BSc(Hons) Computer Science with Mathematics with Year long work placement (Year 4)
 USCMAFB01 : BSc Computing (Year 3)
 USCMAKB01 : BSc Computing with Year long work placement (Year 4)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
 TSMAAFM09 : MSc Mathematical Sciences
 TSMAAPM09 : MSc Mathematical Sciences
 TSMAAFM08 : MSc Modern Applications of Mathematics
 TSMAAWM14 : MSc Modern Applications of Mathematics
 TSMAAFL02 : PG Dip Modern Applications of Mathematics
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
