Numerical Linear Algebra, 6 credits

Numerisk linjär algebra, 6 hp

TANA15

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Fredrik Berntsson

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 110 h

Available for exchange students

Yes
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Applied Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Financial Mathematics) 8 (Spring 2017) 1 1 Swedish/English Linköping C
6CDDD Computer Science and Engineering, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6CMJU Computer Science and Software Engineering, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish Linköping E
6CITE Information Technology, M Sc in Engineering 8 (Spring 2017) 1 1 Swedish/English Linköping E
6MMAT Mathematics, Master's programme 2 (Spring 2017) 1 1 Swedish/English Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Computer Science and Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Mathematics, Master's programme
  • Information Technology, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Computer Science and Software Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Basic course in scientific computing/numerical methods and a course in linear algebra.

Intended learning outcomes

The course is intended to provide basic knowledge about important matrix decompositions; such as the LU or SVD decompositions, and show how matrix decompositions can be used for analyzing and solving both practical and theoretical problems. The course also covers various important techniques from Linear Algebra, such as the Shur complement, convolutions, polynomial manipulation, or orthogonal basis generation. Both linear, and non-linear, least squares problems are also discussed in the course.
After the course students should be able to:

  • Discuss the most common matrix factorizations, and explain their properties.
  • Understand how the most common matrix factorizations are computed; and implement numerical algorithms for computing the most important factorizations.
  • Use matrix factorizations for solving both theoretical problems and practical problems from applications.
  • Discuss the usage of Linear Algebra techniques when solving important application problems, such as pattern recognition, data compression, signal processing, search engines, or model fitting.

Course content

  • Linear algebra: LU-decomposition, SVD, psuedoinvers, orthogonal transformations, Householder transformations, projections, QR-factorisation and least squares problems.
  • Eigenvalues: Normal forms, perturbation theory, Rayleigh quotient, the power method, invers iteration, transformation to Hessenberg and tridiagonal form, QR-iteration.
  • Non-linear system of equations and least squares problems: Newton's and Gauss-Newton's methods.

    Teaching and working methods

    Computer laborations, lectures, exercises, projects and seminars

    Examination

    LAB1Laboratory work2 creditsU, G
    TEN1Written examination4 creditsU, 3, 4, 5
    The first three course aims are examined with TEN1. The fourth and fifth are examined with LAB1.

    Grades

    Four-grade scale, LiU, U, 3, 4, 5

    Department

    Matematiska institutionen

    Director of Studies or equivalent

    Ingegerd Skoglund

    Examiner

    Fredrik Berntsson

    Course website and other links

    http://courses.mai.liu.se/GU/TANA15

    Education components

    Preliminary scheduled hours: 50 h
    Recommended self-study hours: 110 h

    Course literature

    M T Heath: Scientific Computing. An Introductory Survey, Second edition, McGraw Hill, 2002.
Code Name Scope Grading scale
LAB1 Laboratory work 2 credits U, G
TEN1 Written examination 4 credits U, 3, 4, 5
The first three course aims are examined with TEN1. The fourth and fifth are examined with LAB1.

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

M T Heath: Scientific Computing. An Introductory Survey, Second edition, McGraw Hill, 2002.

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X

                            
1.2 Fundamental engineering knowledge (G1X level)
X

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X

                            
3.2 Communications
X

                            
3.3 Communication in foreign languages

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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