FMNN02F

Discontinued

Introduction to Numerical Linear Algebra

7.5

Course given jointly for second and third cycle

FMNN01, NUMA11

7154 (Centre of Mathematical Sciences / Numerical Analysis)

FMNN01, NUMA11

2019-09-12

Professor Thomas Johansson

English

Every autumn semester

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.

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.

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.

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.

Lectures

Project

Oral exam

Written assignments

Weekly hand-in assignments.

Failed, pass

Calculus in several variables. Linear algebra including eigenvalues/vectors. Programming in Matlab or Python.

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

FMNN02F

2019-09-12

Professor Thomas Johansson