Introduction to Numerical Linear Algebra
Introduktion till numerisk linjär algebra

FMNN02F, 7.5 credits

Valid from: Autumn 2019
Decided by: Professor Thomas Johansson
Date of establishment: 2019-09-12

General Information

Division: Numerical Analysis
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course codes: FMNN01, NUMA11
Teaching language: English

Aim

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.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to explain the concept of matrix norm
• be able to account for how one finds the singular value decomposition of a matrix, and to give examples of applications of the decomposition.
• be able to define the condition number of a matrix and to explain its relevance for the solution of systems of linear equations
• be able to describe common methods to numerically determine eigenvalues.

Competences and Skills

For a passing grade the doctoral student must

• be able to implement given algorithms from numerical linear algebra in computer programs and use them to solve problems.
• be able to, in a well-structured report, account for the solution to a problem within the scope of the course.

Course Contents

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.

Course Literature

Trefethen, Lloyd N. & David Bau, I.: Numerical Linear Algebra. SIAM, 1997. ISBN 9780898713619.

Instruction Details

Types of instruction: Lectures, project

Examination Details

Examination formats: Oral exam, written assignments. Weekly hand-in assignments.
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: Calculus in several variables. Linear algebra including eigenvalues/vectors. Programming in Matlab or Python.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page: http://ctr.maths.lu.se/na/courses/FMNN01/