Valid from: Spring 2024
Decided by: Maria Sandsten
Date of establishment: 2023-10-26
Division: Numerical Analysis
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMNN01
Teaching language: English
The aim of the course is to make the postgraduate student familiar with concepts and methods from numerical linear algebra. In general there are ready-made program libraries available but it is important to be able to recognize types of input which may cause problems for the most common methods.
Knowledge and Understanding
For a passing grade the doctoral student must have demonstrated substantially better and more useful knowledge of numerical linear algebra than students who only have completed a regular basic course in scientific computing or linear algebra.
Competences and Skills
For a passing grade the doctoral student must be able to implement algorithms for numerical linear algebra algorithms as computer code and to use them to solve applied problems.
Judgement and Approach
For a passing grade the doctoral student must write logically well-structured reports, in adequate terminology, on weekly homework dealing with the construction and application of advanced algorithms in linear algebra.
Norms. Singular value decomposition and numerical rank. QR factorization, the Gram-Schmidt process and Householder matrices. Least squares problems and pseudoinverses. Linear systems of equations and condition numbers. Positive definite matrices and Cholesky factorization. Numeric determination of eigenvalues.
Trefethen, Lloyd N. & David Bau, I.: Numerical Linear Algebra. SIAM, 1997. ISBN 9780898713619.
Type of instruction: Lectures. Voluntary assignments are given during the course. Feedback is given to those who hand in solutions.
Examination format: Oral exam
Grading scale: Failed, pass
Assumed prior knowledge: Calculus in several variables. Linear algebra including eigenvalues/vectors. Programming in Matlab or Python.
Web page: https://canvas.education.lu.se/courses/20394