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: |
|
Assessment Summary: | CWRI 25%, EXCB 75% |
Assessment Detail: |
|
Supplementary Assessment: |
|
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:
|
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
|
Notes:
|