Course contents *

• Well-posed and ill-posed problems and conditioning of problems
• Rounding errors and numerical stability
• Linear systems of equations: direct methods, sparse matrices
• Singular value decomposition and its application in data analysis and information retrieval
• Eigenvalue problems: theory, orthogonal transformations, iterative methods
• Iterative methods for large linear systems: stationary iterations, Krylov space methods, preconditioning.

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 *

The overall goal of the course is to give you a deeper
understanding of the construction and functioning of modern software for problems. You will be able to select and utilize modern computing routines from a practical problem.

After the course you will be able to

• identify linear algebra computations in a practical problem;
• select appropriate algorithms;
• perform such computations and estimate the computer resources needed;
• judge the quality of the results, and
  implement special algorithms adapted to the problem at hand.

Course Disposition

No information inserted

Specific prerequisites *

Single course students: 90 university credits including 45 university credits in Mathematics or Information Technology. English B, or equivalent.

Recommended prerequisites

Basic numerical analysis, equivalent to DN1212 Numerical Methods and Basic Programmingor
DN1240 Numerical Methods Basic Course II and DN2221 Applied Numerical Methods, part 1. DN2221 is given in period 1 and period 2 so it is ok if you have started that course but not yet finished it.

Equipment

No information inserted

Literature

James W. Demmel: Applied Numerical Linear Algebra, SIAM 1997.
Material on current problems and methods distributed at course.

Grading scale *

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

Examination *

• LAB1 - Laboratory Work, 3.0 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.

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Other requirements for final grade *

Lab reports and written quiz (LAB1; 3 hp)

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Christina Marianne Carlsund Levin

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Offered by

SCI/Mathematics

Main field of study *

No information inserted

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Christina (Ninni) Carlsund, e-post: ninni@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.