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6FMAI13 Linear Algebra

Course Aims

The course is intended to give insight into the most important algorithms and techniques from computational linear algebra. For dense matrices the implementation of basic operations, such as matrix-matrix multiplication and the LU decomposition, and algorithms and theory used for computing common matrix decompositions, such as QR, SVD, or the Eigenvalue decomposition, are included in the course. Applications are used to illustrate the theory and algorithms.

For sparse matrices iterative methods for solving linear systems of equations are treated. This include Classic and Krylov subspace methods, and also preconditioning. Sparse methods for computing eigenvalues and solving least squares methods are also discussed.


The Lectures give an overview of the theory. To each Lecture a set of problems, intended to illustrate the theory, is provided. The Computer exercises give practical experience with implementing and using the methods.


In order to pass the course correctly written solutions to at least half the problems have to be handed in. Also all the computer exercises needs to be completed.

Sidansvarig: Fredrik Berntsson
Senast uppdaterad: 2020-06-24