FMNN01F

Temporary

Numerical Linear Algebra

7.5

Course given jointly for second and third cycle

7154 (Centre of Mathematical Sciences / Numerical Analysis)

2023-10-26

Maria Sandsten

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.

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.

be able to implement algorithms for numerical linear algebra algorithms as computer code and to use them to solve applied problems.

write logically well-structured reports, in adequate terminology, on weekly homework dealing with the construction and application of advanced algorithms in linear algebra.

Lectures

Voluntary assignments are given during the course. Feedback is given to those who hand in solutions.

Oral exam

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.

FMNN01F

2023-10-26

Maria Sandsten