| TANA15 |
Numerical Linear Algebra, 6 ECTS credits.
/Numerisk linjär algebra/
For:
D
IT
MMAT
Y
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Prel. scheduled
hours: 50
Rec. self-study hours: 110
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Area of Education: Natural Science
Main field of studies: Mathematics, Applied mathematics
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Advancement level
(G1, G2, A): A
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Basic course in scientific computing/numerical methods and a course in linear algebra.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Computer laborations, lectures, exercises, projects and seminars
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Course contents:
- 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.
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Course literature:
M T Heath: Scientific Computing. An Introductory Survey, Second edition, McGraw Hill, 2002.
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Examination: |
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Written examination
Laboratory work
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4 ECTS
2 ECTS
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The first three course aims are examined with TEN1. The fourth and fifth are examined with LAB1. |
Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Fredrik Berntsson
Link to the course homepage at the department
Course Syllabus in Swedish
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