Department of Applied Mathematics and Theoretical Physics

Numerical Analysis Course

QR - Click & Kill

Contents

Introduction

Householder and Givens rotations are important for introducing zeros in calculating the QR factorisation. This module allows you to play with these transformations to introduce zeros wherever you like, not just below the main diagonal.

Review

Revisit the module QR Factorisation if you need to review Householder reflections and Givens rotations.

The GUI

Running the downloadable MATLAB code on this page opens a GUI which allows you to experiment with the effects of Householder and Givens transformations on a matrix of your choice. The matrix must be square.

QR_click_n_kill

To activate the GUI, click once on the matrix. You will see a crosshair appear on the screen. Now you can select any entry of the matrix.

Note: You must always click once to activate the crosshairs before you proceed with any of the following

When Householder method (the default method) is selected, if you click on the entry $(i,j)$, the program will clear ("kill") all the entries in the $j$-th column below the selected entry. So, for example, if you want to clear the all the entries in the 3rd column below the main diagonal, you would have to click on the (3,3)-th entry of the matrix.

When Givens method is selected, you will have to first click to choose the entry you want to clear, and then click to choose which row you want to use to clear your chosen entry. For example, if you want to clear the (2,4)-th entry by using the 3rd row, you would have to first click on the (2,4)-th entry, and then click on any entry in the 3rd row.

You might want to try the GUI with the matrix given in exercise 7 on Example Sheet 3.

References

[1] http://en.wikipedia.org/wiki/QR_decomposition

The Code

All files as zip archive: qr_click_all.zip