## TANA15 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: The QR factorization and applications.

In this exercise we first compute the QR factorization using Householder reflections. Then we use Givens rotations to solve the row updating problem. An application is given.

Instructions: E1-TANA15-QR-and-Applications.pdf
Matlab: ApplyReflection.m, HouseholderQR.m, QRUpdate.m and CometTracking.m.

#### Exercise 2: Computing Eigenvalues

Firstly the Power method is used to compute eigenvalues. Secondly, a practical Matlab implementation of the QR algorithm is done. An application example is also solved.

Instructions: E2-TANA15-Eigenvalues.pdf
Matlab: EigPower.m, Hessenberg.m and HessEigQR.m.

#### Exercise 3: Nonlinear Equations and Least Squares

In this exercise we compare Newtons and Broyden's methods for solving a, rather complicated, nonlinear equation.

Instructions: E3-TANA15-Nonlinear.pdf
Matlab: EqSolveNewton.m, SoccerODE.m, BallAcceleration.m, BallJacobian.m, HitGroundEvent.m, DisplayTrajectory.m, FindFinalPosition.m, CircleData.m and GaussNewton.m.

#### Exercise 4: Applications of the SVD

Instructions: E4-TANA15-SVD.pdf
Matlab: Goose.mat, DataSet.mat, DisplayDigit.m and ExtractDigits.m.

Page responsible: Fredrik Berntsson
Last updated: 2020-01-21