*Course Syllabus for*
# 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.

**Types of instruction:** Lectures, project

**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

**Course coordinators:**

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