*Course Syllabus for*
# Numerical Linear Algebra

Numerisk linjär algebra

## FMNN01F, 7.5 credits

**Valid from:** Spring 2024

**Decided by:** Maria Sandsten

**Date of establishment:** 2023-10-26

## 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 code:** FMNN01

**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
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.

## 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.

**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

**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:** https://canvas.education.lu.se/courses/20394