# TMA4205 - Numerical Linear Algebra

### Examination arrangement

Examination arrangement: Aggregate score

Evaluation Weighting Duration Grade deviation Examination aids
Project 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 and exercises (with or without presentations). The exercises require the use of a computer. Some of the exercises will be compulsory.

• 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 To
SIF5043 7.5
More on the course
Facts

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

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2024

Language of instruction: English

Location: Trondheim

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

Department of Mathematical Sciences

# Examination

#### Examination arrangement: Aggregate score

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD School exam 70/100 2024-12-17 15:00
Autumn ORD Project 30/100
Summer UTS School exam 70/100
• * 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.
Examination

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

More on examinations at NTNU