## 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