mm245/ma260 lab2

mm245/ma260 lab2

http://www.maths.nuigalway.ie/~gettrick/teach/mm245/labs/l2.html

As well as coming to the supervised lab - you are expected to work on this lab on your own outside of lab hours (in your own time).
For this lab you must submit all source code (matlab/scilab/octave .m files). The code should have comments of explanation, with at least as many comments as code. This should be sent in via BLACKBOARD (not directly by email). Any questions asked should be answered by typing into a plain text (.txt) file (or inserted at the end of MATLAB/SCILAB/OCTAVE code after the percentage (comment) symbol) which should also be uploaded via blackboard.
This material should be uploaded before the deadline of 5pm Friday October 11th, 2013. You will lose 20% for each day (or part of day) the lab is late.
Plagiarism (the unattributed copying of work from other sources (internet, fellow students,....)) will not be tolerated. Please see http://www.nuigalway.ie/engineering/documents/plagiarism_guide_students _v4.pdf. You risk getting zero for your lab if it is found to be plagiarized.
If you are really stuck:

Ask in the lab
Post a question in the Discussion Board in BLACKBOARD

You should first read the code in fixedp1.m at http://www.maths.nuigalway.ie/~gettrick/teach/mm245/labs/matlab/ and try to understand it. For this lab

Consider the "problem" of finding the square root of two, i.e. the root of f(x)=x**2-2. Consider the fixed point iterations

g₁(x) = x/2 + 1/x
g₂(x) = 2*x/3 + 2/(3*x)

Calculate the order of convergence for both g₁(x) and g₂(x). (You don't need MATLAB/SCILAB/OCTAVE to do this!)

Write MATLAB code to carry out iterations using g₁(x) starting at the point x₀ = 100. How many iterations are needed to obtain the square root of two to 9 decimal places (i.e. 1.414213562)?

Write MATLAB code to carry out iterations using g₂(x) starting at the point x₀ = 2. How many iterations are needed to obtain the square root of two to 9 decimal places (i.e. 1.414213562)?

For your second MATLAB program (using g₂(x)): Determine the relative error at each step in your calculation, using 1.414213562 as the actual square root of two.