course-details-portlet

TMA4205

Numerical Linear Algebra

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Credits 7.5
Level Second degree level
Course start Autumn 2024
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement Aggregate score

About

About the course

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 and exercises (with or without presentations). The exercises require the use of a computer. Some of the exercises will be compulsory.

Compulsory assignments

  • Exercises

Further on evaluation

All partial evaluations must be passed in order to receive a grade in the course.

Retake of examination may be given as an oral examination. The retake exam is in August.

Students are free to choose Norwegian or English for written assessments.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From
SIF5043 7.5 sp
This course has academic overlap with the course in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics
  • Technological subjects

Contact information

Course coordinator

Lecturers

Department with academic responsibility

Department of Mathematical Sciences