TMA4205 - Numerical Linear Algebra

About

Examination arrangement

Examination arrangement: Portfolio assessment
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Work 30/100
Written examination 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 and flexible preconditioning; (9) explain the fundamental ideas behind multigrid and 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 they are attended by students from the Master's Programme in Mathematics for International students. 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

Specific conditions

Exam registration requires that class registration is approved in the same semester, or that compulsory activities are approved in a previous semester.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5043 7.5

Timetable

Examination

Examination arrangement: Portfolio assessment

Term Evaluation form Weighting Examination aids Date Time Room *
Autumn Written examination 70/100 C
Autumn Work 30/100
* 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.