TMA4205 - Numerical Linear Algebra


Examination arrangement

Examination arrangement: Portfolio assessment
Grade: Letters

Evaluation Weighting Duration Grade deviation Examination aids
Work 30/100
School exam 70/100 4 hours C

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

A student successfully meeting all the learning objectives of this course will be able to: (1) explain and fluently apply fundamental linear algebraic concepts such as matrix norms, eigen- and singular values and vectors; (2) estimate stability of the solutions to linear algebraic equations and eigenvalue problems; (3) recognize matrices of important special classes, such as normal, unitary, Hermitian, positive definite and select efficient computational algorithms based on this classification; (4) transform matrices into triangular, Hessenberg, tri-diagonal, or unitary form using elementary transformations; (5) utilize factorizations and canonical forms of matrices for efficiently solving systems of linear algebraic equations, least squares problems, and finding eigenvalues and singular values; (6) explain the underlying principles of several classic and modern iterative methods for linear algebraic systems, such as matrix-splitting, projection, and Krylov subspace methods, analyze their complexity and speed of convergence based on the structure and spectral properties of the matrices; (7) explain the underlying principles of iterative algorithms for computing eigenvalues of small and select eigenvalues of large eigenvalue problems; (8) explain the idea of preconditioning; (9) explain the fundamental ideas behind multigrid and/or domain decomposition methods; (10) estimate the speed of convergence and computational complexity of select numerical algorithms; (11) implement select algorithms on a computer.

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 projects (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 the course is attended by students who don't master a Scandinavian language. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Compulsory assignments

  • Exercises

Further on evaluation

In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety. Submitted work that counts towards the final grade will also have to be retaken. For more information about grading and evaluation. see «Teaching methods and activities».

Specific conditions

Compulsory activities from previous semester may be approved by the department.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5043 7.5
More on the course

Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  AUTUMN 2021

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
  • Mathematics
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences


Examination arrangement: Portfolio assessment

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD School exam 70/100 C 2021-12-14 15:00
Room Building Number of candidates
SL510 Sluppenvegen 14 15
Autumn ORD Work 30/100 INSPERA
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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