mm245/ma260 lab5

mm245/ma260 lab5

http://www.maths.nuigalway.ie/~gettrick/teach/mm245/labs/l5.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 November 22nd, 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 study (and run) the code in jacobi.m at http://www.maths.nuigalway.ie/~gettrick/teach/mm245/labs/matlab/ which is commented to explain its operation.

Write a function in MATLAB/SCILAB/OCTAVE that calculates the distance between two vectors v₁ and v₂.

Using your function, program in MATLAB a Jacobi iterative scheme to solve the system of equations here. You should start with an initial vector x⁽⁰⁾ of all zeros, and terminate when the distance between successive estimates is less than 0.003.

How many iterations do you need to get error less than 0.003?
From your numerical estimates - can you "guess" the actual solution (given that they are all integers)? Check your answer and submit it.

Write a function in MATLAB to test whether or not a matrix is strictly diagonally dominant. (You should test your function on the 8x8 matrix from the previous part).