Course content

The course focuses on iterative techniques for solving large sparse linear systems of equations which typically stem from the discretisation of partial differential equations. In addition, computation of eigenvalues, least square problems and error analysis will be discussed.

Learning outcome

1. Knowledge. The student has knowledge of the basic theory of equation solving and modern methods for solving large sparse systems and to find eigenvalues of such systems. The student understands the mechanisms underlying projection methods and Krylov methods in general, and has detailed knowledge about selected algorithms. The student understands the principle of preconditioning and understands selected techniques in detail. The student is familiar with the practical use of matrix factorization techniques and has detailed knowledge of techniques for calculating eigenvalues of matrices.

2. Skills. The student is able to implement selected algorithms for a given model problem, and can assess the performance and limitations of the various methods. The student can make qualified choices of linear equation solvers/eigenvalue algorithms for specific types of systems. The student can assess the complexity and accuracy of the algorithms used.

3. General competence. The student can describe a chosen scientific method and communicate his or her findings in a written report using precise language.

Learning methods and activities

Lectures, projects-/semester problem and exercises. The exercises demand the use of a computer. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (70%) and exercises (30%). The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course is based on TMA4145 Linear Methods or equivalent. TMA4215 Numerical Mathematics is recommended, but not mandatory.

Course materials

Will be announced at the start of the course.

Credit reductions