DN2253 Numerical Algebra, Methods for Large Matrices 7.5 credits

Numerisk algebra för stora matriser

This course is the later moments of 2D1252/DN2252, Numerical Algebra.

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

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.

Intended learning outcomes *

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.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

No information inserted

Recommended prerequisites

Corresponding to 2D1250/DN2250 or 2D1251/DN2251, Applied numerical analysis II or III.

Equipment

No information inserted

Literature

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

Material on current problems and methods distributed at course.

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

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

Other requirements for final grade *

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

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

Michael Hanke

Further information

Course web

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Offered by

SCI/Mathematics

Main field of study *

No information inserted

Education cycle *

Second cycle

Add-on studies

2D1263 Scientific Computing, 2D1290 /DN2290Advanced Numerical Methods.

Contact

Michael Hanke, tel: 790 6278, e-post:hanke@nada.kth.se

Ethical approach *

  • 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.

Supplementary information

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.