MA50178: Numerical linear algebra
[Page last updated: 03 August 2022]
Academic Year:  2022/23 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  CW 40%, EX 60% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  
Learning Outcomes:  : Students should know a range of modern iterative methods for solving linear systems, the algebraic eigenvalue problem and least squares problems. They should be able to analyse their algorithms and should have an understanding of relevant practical issues. 
Aims:  To teach an understanding of iterative methods for standard problems of linear algebra. 
Skills:  Problem Solving (T,F&A), Computing (T,F&A), independent study and report writing. 
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. Least squares problems: Fullrank and rankdeficient least squares problems, Normal equations, QR decompostion, Singular value decompostion, lowrank approximation and applications. 
Programme availability: 
MA50178 is Optional on the following programmes:Department of Mathematical Sciences

Notes:
