SF2524 Matrix Computations for Large-scale Systems 7.5 credits

Matrisberäkningar för storskaliga system

In this course we will learn some of the most common numerical techniques and algorithms used to efficiently solve problems  expressed using large matrices.

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Course information

Content and learning outcomes

Course contents *

  • Fundamentals of matrix computations: Floating point arithmetic, computational complexity, representation of matrices.
  • Iterative and direct methods for linear systems of equations: large, structured and sparse systems.
  • Iterative methods for eigenvalue problems: full matrices, large and sparse matrices, other structures, applications.
  • Methods for large-scale dynamical systems: stability, model reduction, and computation of Gramian.
  • Algorithms for matrix functions: direct methods, iterative methods and applications.

Intended learning outcomes *

After having completed the course the student will understand the principles of computations with matrices. Moreover, the student will be able to select, implement, apply andanalyze the most important matrix methods suitable for the matrix problems stemming from particular applications.

  • The student should be able to setup and formulate the matrix problems stemming from a applications in, for instance systems and control, acoustics, or quantum chemistry.
  • The student will be able to select an appropriate matrix representation and select an algorithm based on the structure of the problem and matrix.
  • The student will be able to derive and implement the most important algorithms for the main problems of the course.
  • The student will be able to relate the theoretical properties of the algorithm, such as error and computation time, with the implementation, output and performance of the algorithm.
  • The student will be able to derive new variants of the algorithms for related problems based on the set of matrix computation tools in the course.

Course Disposition

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Literature and preparations

Specific prerequisites *

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

Recommended prerequisites

SF2520 Applied Numerical Methods (or equivalent), can be read in parallel.

Equipment

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Literature

Course literature will be announced at least 4 weeks before course start at course web page.

Examination and completion

Grading scale *

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

Examination *

  • LABA - Laboratory, 3.5 credits, Grading scale: P, F
  • TEN1 - Examination, 4.0 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.

Other requirements for final grade *

  • Laborations completed (LABA)
  • Written Exam completed (TEN1)

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

Elias Jarlebring

Further information

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.

Course web SF2524

Offered by

SCI/Mathematics

Main field of study *

Mathematics, Technology

Education cycle *

Second cycle

Add-on studies

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Contact

Elias Jarlebring (eliasj@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

Course literature will be announced at least 4 weeks before course start at course web page.