DN2253 Numerical Algebra, Methods for Large Matrices 7.5 credits

Linear systems of equations: direct algorithms, perturbation theory and condition, rounding errors. Sparse matrices.

Iterative methods: stationary iterations, Krylov space methods and preconditioning.

Eigenvalue problems: theory, transformation methods and iterative methods.

Singular value decomposition and its applications in data analysis and information retrieval.

Model reduction for linear and nonlinear dynamical systems.

For each algorithm it is studied how it works, how many resources that are used as well as how good accuracy that can be expected in the results.

After having completed the course the student should realize how linear algebra is depending on computer resources and accuracy when performing a scientific computation. The student should also be able to utilize modern computing routines from linear algebra in a practical problem.

After the course the student should be able to

• identify linear algebra computations in a practical problem
• perform such a computation, estimate computer resources and judge the quality of the results
• implement special algorithms adapted to the properties of the problem
• design the algorithm so that that the machine architecture of the computers can be utilized.

James W. Demmel: Applied Numerical Linear Algebra, SIAM 1997.

Material on current problems and methods distributed at course.

• TENB - Examination, 4.5 credits, grading scale: A, B, C, D, E, FX, F
• LABB - Laboratory Work, 3.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

If the course is discontinued, students may request to be examined during the following two academic years.

Computer assignments (LAB1; 3 university credits).
Oral final exam (TEN1; 4,5 university credits).

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

You can only count one of the courses 2D1252/DD2252 Numerisk algebra and 2D1253/DD2253 Numerical Algebra, Methods for Large Matrices in your degree.

The course can be held in english if the participants wish.

The course is given every second year.