Numerical Linear Algebra ENMTMA265 and GUMMA600 7.5 credit points
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For homeworks and computer exercises, see section Programme
Obs! Participation at least 50% of lectures at this course is necessary!
All students should register for this course. For registration see antagning.se
All examination works written at 25.10.2016 are verified and you can get information about your grades at expedition. Ask personal at expedition about information in LADOK.
Answers to the questions at examination are here:
Answers for examination at 25.10.2016
Already is known that reexamination will be at 05.01.2017, 14:0018:00, Maskinhuset.
Here are some available topics for Master works:
High Performance Scientific software for the solution of Helmholtz equation
Parameter identification in mathematical model of HIV infection with drug therapy
Optimization approach in the design of approximate cloaking structures
I thank all of You who will answer to the following course evaluation survey (I assume that it is only for students at Chalmers, but GU students can fill out course evaluation from GUpage):
Course evaluation survey
This survey helps me get feedback from You and improve course for the next time.
I will be very grateful if You can fill it.
Contents:
Problems of numerical linear algebra arise in many different fields of
science like computational fluid dynamics, solid mechanics, electrical
networks, signal analysis, and optimisation. In this course we study
basic linear algebra concepts like matrix algebra, theory for linear
systems of equations, spectral theory, and vector and matrix norms as
well as numerical aspects like efficiency, reliability, error analysis
and condition numbers. We will study following topics:
 For solving linear systems of equations we will present Gaussian
elimination with different pivoting strategies and blocking algorithms
for higher performance using BLAS (basic linear algebra
subroutines).
 For leastsquares problems we study
QRfactorisation and Singular Value Decomposition
(SVD).
 The methods for solution of eigenvalue problems which are based on transformation
techniques for symmetric and nonsymmetric matrices.
 The basic iterative methods (Jacobi, GaussSeidel and Successive overrelaxation (SOR)) for solution of linear systems.
 Introduction to the Krylov subspace methods.
For all topics above we will discuss numerical algorithms with respect to applicability, reliability, accuracy, and efficiency.
By implementing computer exercises in MATLAB and C++/PETSc the students will get experience in implementation and evaluation of numerical algorithms for problems of
linear algebra.
By the completion of this course the students will be able to:
 use numerical linear algebra as building bricks in computation.
 make a linear algebra model of problems from the physical reality.
 derive and use the numerical techniques needed for a professional solution of a given linear algebra problem.
 use computer algorithms, programs and software packages to compute solutions to current problems.
 critically analyze and give advice regarding different choices of models, algorithms, and software with respect to efficiency and reliability.
 critically analyze the accuracy of the obtained numerical result and to present it in a visualized way.
The course consists of 36 lecture hours, 20 exercise hours and gives 7.5 points.
The course code for engineering schools and students registered at Chalmers is TMA265. The course code for students registered in GU is MMA600.
All current and recent information will be
placed here. Regarding examination : CTH students should
not register for this exam. Only GU students can register for the
examination. CTH and GU students will get their personal exam numbers from
Observers of this exam. Examination usually is at Maskinhuset at
Chalmers:
Maskinhuset Where exactly (in which one
room) will be exam You will know at the day of examination: the
announcement will be placed at the blackboard close to the entree of
Maskinhuset. Notes: GU students can do reexamination but they can not
high their scores (for example, from G to VG) but Chalmers students
can do reexamination and high scores. Please, follow this site to get
exact information when and where will be reexamonation closer to the
day of reexamination.
Wednesdays 1315 (except the first week) in computer room MVF24 (Mathematical Sciences in Physics building).
Fridays 1315 in computer room MVF24 (exept the first week).
Computer labs and Matlab/PETSc excercises will be included in the
assignments below.
Matlab programs which will be used in computer exercises:
Poisson2D_LU.m
DiscretePoisson2D.m
BackSub.m
ForwSub.m
LU_factor.m
Templates for programs written in PETSc:
Template for computing of discretized Laplacian
Template for the main program in PETSC for LU decomposition
Example of Makefile to be able compile PETSc program at Chalmers
Template for petsc function which removes zeros from the original matrix. We can work then with resulting matrix without zeros in the same way as with original matrix.
Additional templates of PETScMakefile and main program in PETSc:
Example of the main program in PETSC.
Example of the Makefile to compile the above main program like that: make hello
Reference literature:
 Tobin A. Driscoll, Learning MATLAB, ISBN: 9780898716832
(The book is published by SIAM)
The following sections in the textbook will be considered in the
book.
 Chapter 1

mainly repetition and brief revision on basic linear algebra.
 Chapter 2

16, 7 except 2.7.4 and 2.7.5
 Chapter 3

15
 Chapter 4

14
 Chapter 5

14
 Chapter 6

16, except 6.3.3, 6.5.6, 6.6.4,6.6.6
The following questions in the textbook are recommended:
 Chapter 1: 1, 2, 3, 4, 5, 7, 13.
 Chapter 2: 3, 6, 7, 10, 11, 12, 17, 19.
 Chapter 3: 1, 2, 3(parts 1,2,3), 4, 5, 6, 8, 9, 11, 14, 15, 18.
 Chapter 4: 1, 3, 4, 5, 6, 7, 10, 11, 12, 13.
 Chapter 5: 1, 3 (for symmetric matrix), 6, 7, 14, 15, 16, 17, 18, 22, 27, 28.
To each chapter belong an optional homework assignment and a
computer exercise. The homework assignments are similar to the
questions in the textbook and such you could expect at the
examination. In the computer exercises you will be trained in using
different algorithms in numerical linear algebra using MATLAB or
PETSc libraries. Either you will use already existing MATLAB and
PETSC programs or write your own small MATLAB or PETSc codes. The
homework assignments give bonus credit points for the examination.
Since the occasions reserved for the computer exercises are without
supervision you may put questions on these exercises to me at the
lectures. Passed computer exercises will be graded with grades 3,
4, or 5, see examination below.
You may work in a group of 2 persons but hand in only one report for the group.
Wednesdays 1315 (except the first week) in computer room MVF24 (Mathematical Sciences at Physics building)
Fridays 1315 in computer room MVF24 (exept the first week when it is in room MVF25).
Hand in a short report of your work
before the final exam.
In
Chalmers Student Portal you can read about when exams are
given and what rules apply on exams at Chalmers.
At the link
Schedule
you can find when exams are given for courses at University of
Gothenburg.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to
take the examination. If you study at Chalmers, you will do this
by the
Chalmers Student Portal, and if you study at University of
Gothenburg, so sign up via
GU's
Student Portal.
You can see your results in Ladok by logging on to the Student
portal.
At the annual examination:
When it is practical a separate review is arranged. The date of
the review will be announced here on the course website. Anyone
who can not participate in the review may thereafter retrieve and
review their exam on Mathematical sciences study expedition,
Monday through Friday, from 9:00 to 13:00. Check that you have the
right grades and score. Any complaints about the marking must be
submitted in writing at the office, where there is a form to fill
out.
At reexamination:
Exams are reviewed and picked up at the Mathematical sciences
study expedition, Monday through Friday, from 9:00 to 13:00. Any
complaints about the marking must be submitted in writing at the
office, where there is a form to fill out.