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.

## Instruction Details

Types of instruction: Lectures, project

## Examination Details

Examination formats: Oral exam, written assignments. Weekly hand-in assignments.