# Exercises

## General Information

We require you to take part in the exercises and deliver your solutions to the tasks distributed in the lectures (see also Criteria). Each Tuesday, a task sheet will be distributed. For those, who missed to get one, we provide online versions of the sheets below. You will also find accompanying material like m-files, data, etc. on these pages. Sometimes, we might give hints for the solution of your tasks.## Helpers

Lars Mentrup has collected two little helpers to get you started with MATLAB and Unix. A very short Intro to UNIX (56kB)A very short Intro to MATLAB (70kB)

## Exercise 1

Here is the task sheet and the MATLAB programs referred to by the sheet. Exercise sheet 1 (75kB)Matlab file oldeps.m (487B)

## Exercise 2

Here is the task sheet. Exercise sheet 2 (74kB)## Exercise 3

Please find the task sheet below. Exercise sheet 3 (69kB) And here is a proof of the formulas for the row-sum, column-sum and spectral matrix norms: Supplement to Exercise sheet 3 (61kB)## Exercise 4

Here is exercise 4: Exercise sheet 4 (92kB)## Exercise 5

An other beautiful sheet: Exercise sheet 5 (59kB) And a MATLAB m-file that allows to see the failure of high order interpolation on Runge's test casePlease Note: I added a modified version that should run now (including

**function polyinterp**)

rungeinterp.m (4KB)

## Exercise 6

In this sheet we will deal with Discrete Fourier Transforms (DFT): Exercise sheet 6 (59kB)MATLAB data file sunspot.dat (4kB) For an example of the solution to the sunspots assignement, see the textbook by C. Moler (see the Literature list or Cleve Moler's online book

^{})

An M-file is also available as part of the book's attached software package (see http://www.mathworks.com/moler/ncm/sunspotstx.m

^{}).

## Exercise 7

In this sheet we will deal with the piecewise interpolation concept: Exercise sheet 7 (65kB)MATLAB data file spline.dat (927B)

MATLAB data file splinedelta.dat (921B)

## Exercise 8

A real life least squares problem, a finite difference error approximation and a quadrature implementation: Exercise sheet 8 (136kB)MATLAB data file delamo.dat (140B)

The solution to the first assignment with a LAPACK interface was hard to get. One possibility is to get the Lapack for MATLAB package and compile the corresponding mex-files. The other possibility is to download my solution in the following zip-file. It works for MATLAB version 7.0.4 on an

*Intel Pentium M*based Laptop. You might want to recompile the two dynamic load libraries (dlls) by issuing the commands

**mex dgeqrf.c**and

**mex dormqr.c**(possibly with appropriate options, see the MATLAB documentation). s8a1_with_mexfiles.zip (9kB)

## Exercise 9

The implementation of an adaptive Simpson quadrature: Exercise sheet 9 (63kB)## Exercise 10

Eigenvalues: Exercise sheet 10 (68kB)MATLAB file plot_pspec.m (2kB) for plotting the pseudo-spectrum