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6FMAI13 Computer Exercises
The computer exercises are to be completed either in a group of
two students, or by one student alone. A written report that answers
all questions should be written (possibly by hand). Include graphs
in the report. The final Matlab programs should be sent by email to
fredrik.berntsson@liu.se.
Exercise 1: Least Squares Problems
In this exercise we will compute the QR decomposition using Householder reflections. Also we will use the QR decomposition to fit an ellipse to given points (xk,yk).
Instructions: E1-TANA15-QR-and-Applications.pdfMatlab: ApplyReflection.m , HouseholderQR.m, QRUpdate.m, CometTracking.m.
Exercise 2: Eigenvalues
The QR is the default choice for computing eigenvalues of non-symmetric matrices. In this exercise the alrogithm will be implemented and tested.
Instructions: E2-TANA15-Eigenvalues.pdfMatlab: Hessenberg.m, HessEigQR.m.
Exercise 2.5: Sylvesters Law of Inertia
In this exercise you will use Sylverster's Law of Inertia to prove simple bounds for the eigenvalues of a symmetric matrix.
Instructions: E2.5-MAI0119-Sylvester.pdfExercise 4: The Singular Value Decomposition
In this exercise the SVD will be used for a small model fitting problem and also for solving a classification problem.
Instructions: E4-TANA15-Singular-values.pdfMaterial: Goose.mat, DataSet.mat, CircleData.m, ExtractDigits.m, DisplayDigit.m, DistanceFromSubspace.m, CreateSubspaces.m and ClassifyDigit.m.
Exercise 4.5: The Conjugate Gradient Method
The Conjugate gradient method is the default choice for solving sparse linear systems with positive definite and symmetric matrices. In this exercise we will implement the method and test its properties.
Instructions: E4.5-Sparse.pdfMaterial: Bundle1.mat.
Sidansvarig: Fredrik Berntsson
Senast uppdaterad: 2020-06-24